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CIRCLES
CIRCLES
A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y − 4 x + 3 = 0, then its radius is equal to :
A B C D2 1
A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y − 4 x + 3 = 0, then its radius is equal to :
A B C D2 1
Solution :
11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics
A B C D6 13
A square is inscribed in the circle x2 + y2 - 6x + 8y - 103 = 0 with its sides parallel to coordinate axes.Then the distance between origin and vertex of this square which is nearest to the origin is
11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics
A square is inscribed in the circle x2 + y2 - 6x + 8y - 103 = 0 with its sides parallel to coordinate axes.Then the distance between origin and vertex of this square which is nearest to the origin is
A B C D6 13
11-01-2019 - Morning Shift - MathematicsSolution :
Equation of circle touching the lines |x - 2| + |y - 3| = 4 will be
A B
C D
(x - 2)2 + (y - 3)2 = 12 (x - 2)2 + (y - 3)2 = 4
(x - 2)2 + (y - 3)2 = 2 (x - 2)2 + (y - 3)2 = 8
Equation of circle touching the lines |x - 2| + |y - 3| = 4 will be
A B
C D
(x - 2)2 + (y - 3)2 = 12 (x - 2)2 + (y - 3)2 = 4
(x - 2)2 + (y - 3)2 = 2 (x - 2)2 + (y - 3)2 = 8
Solution :
x - y = 3
The equation of the image of the circle x2 + y2 + 16x - 24y + 183 =0 in the line mirror 4x + 7y + 13 = 0 is
A B
C D
x2 + y2 + 32x - 4y + 235 = 0 x2 + y2 + 32x + 4y - 235 = 0
x2 + y2 + 32x - 4y - 235 = 0 x2 + y2 + 32x + 4y + 235 = 0
The equation of the image of the circle x2 + y2 + 16x - 24y + 183 =0 in the line mirror 4x + 7y + 13 = 0 is
A B
C D
x2 + y2 + 32x - 4y + 235 = 0 x2 + y2 + 32x + 4y - 235 = 0
x2 + y2 + 32x - 4y - 235 = 0 x2 + y2 + 32x + 4y + 235 = 0
Solution :
09-01-2020-Morning Shift
A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle?
A B
C D
4x – 3y + 17 = 0 3x – 4y – 24 = 0
3x + 4y – 6 = 0 4x + 3y – 8 = 0
09-01-2020-Morning Shift
A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle ?
A B
C D
4x – 3y + 17 = 0 3x – 4y – 24 = 0
3x + 4y – 6 = 0 4x + 3y – 8 = 0
Solution :
12-04-2019-Evening Shift
A circle touching the X-axis at (3, 0) and making an intercept of length 8 on the Y-axis passes through the point :
A B C D(3, 10) (3, 5) (2, 3) (1, 5)
12-04-2019-Evening Shift
A circle touching the X-axis at (3, 0) and making an intercept of length 8 on the Y-axis passes through the point :
A B C D(3, 10) (3, 5) (2, 3) (1, 5)
Solution :
08-04-2019-Morning Shift
The sum of the squares of the lengths of the chords intercepted on the circle, x2 + y2 = 16, by the lines, x + y = n, n ∈ N, where N is the set of all natural numbers, is :
Solution :
The tangent to the circle C1 : x2 + y2 – 2x – 1 = 0 at the point
(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is ..
A B C D2 3
The tangent to the circle C1 : x2 + y2 – 2x – 1 = 0 at the point
(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is ..
The tangent to the circle C1 : x2 + y2 – 2x – 1 = 0 at the point
(2, 1) cuts off a chord of length 4 from a circle C2, whose centre is (3, -2). The radius of C2 is :
A B C D2 3
Solution :
11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics
The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :
A B C D
11-01-2019 - Morning Shift - Mathematics11-01-2019-Morning Shift - Mathematics
The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :
A B C D
11-01-2019 - Morning Shift - MathematicsSolution :
08-01-2020-Evening Shift
If a line, y = mx + c is a tangent to the circle, ( x – 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point ; then
A B
C D
c2 + 7c + 6 = 0 c2 + 6c + 7 = 0
c2 – 6c + 7 = 0 c2 – 7c + 6 = 0
08-01-2020-Evening Shift
If a line, y = mx + c is a tangent to the circle, ( x – 3)2 + y2 = 1 and it is perpendicular to a line L1, where L1 is the tangent to the circle, x2 + y2 = 1 at the point ; then :
A B
C D
c2 + 7c + 6 = 0 c2 + 6c + 7 = 0
c2 – 6c + 7 = 0 c2 – 7c + 6 = 0
Solution :
08-04-2019-Evening Shift
The tangent and the normal lines at the point to the circle x2 + y2 = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :
A B C D
08-04-2019-Evening Shift
The tangent and the normal lines at the point to the circle x2 + y2 = 4 and the x-axis form a triangle. The area of this triangle (in square units) is :
A B C D
Solution :
10-04-2019-Evening Shift
A B
C D
The locus of the centres of the circles, which touch the circle x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is:
10-04-2019-Evening Shift
The locus of the centres of the circles, which touch the circle x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is:
A B
C D
Solution :
The locus of the centre of a circle which touches externally the circle (x - 3)2 + (y - 3)2 = 4 and also touches the y-axis is given by the equation:
A B
C D
x2 - 6x - 10y + 14 = 0 x2 - 10x - 6y + 14 = 0
y2 - 6x - 10y + 14 = 0 y2 - 10x - 6y + 14 = 0
The locus of the centre of a circle which touches externally the circle (x - 3)2 + (y - 3)2 = 4 and also touches the y-axis is given by the equation:
A B
C D
x2 - 6x - 10y + 14 = 0 x2 - 10x - 6y + 14 = 0
y2 - 6x - 10y + 14 = 0 y2 - 10x - 6y + 14 = 0
Solution :
09-01-2020-Evening Shift
If the curves, x2 - 6x + y2 + 8 = 0 and x2 - 8y + y2 + 16 - k =0, (k > 0) touch each other at a point, then the largest value of k is
Solution :
09-01-2019-Evening Shift
If the circles x2 + y2 – l6x – 20y + 164 = r2 and (x – 4)2 + (y – 7)2 =36 intersect at two distinct points, then:
A B C Dr > 11 0 < r < 1 r = 11 1 < r < 11
09-01-2019-Evening Shift
If the circles x2 + y2 – l6x – 20y + 164 = r2 and (x – 4)2 + (y – 7)2 =36 intersect at two distinct points, then:
A B C Dr > 11 0 < r < 1 r = 11 1 < r < 11
Solution :
Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle when
A B
C D
All are integral values of K 0 < K < 1
K < 0 For two values of K
Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle when
A B
C D
All are integral values of K 0 < K < 1
K < 0 For two values of K
Solution :
If a circle passes through the points of intersection of the coordinate axes with the lines λx - y + 1 = 0 and x - 2y + 3 = 0, then the value of λ is
A B C D2 4 6 3
If a circle passes through the points of intersection of the coordinate axes with the lines λx - y + 1 = 0 and x - 2y + 3 = 0, then the value of λ is
A B C D2 4 6 3
Solution :
Leaderboard
Vaibhav Dubey Aditya Barkataky
Simran Abhay Srivastava
Teju Aquasa Aziz
Darshan Abhiraj Patil
Amit Raj Sinha Parth Bhatnagar
Aadish Jain Varun Gyanchandani
Pranjal Ambwani Shaharyar Ansari
Armaan Mittal Nitin Jha
Janvi Patel Reeti
Harshavardhan Pawar Aditya Ojha
Chirayu Jadhav Lakshay kumawat
Siddharth Goyal Juhi Juhi
Siddharth Tiwari Khushi Agarwal
Tatva Mohammed Abdulla
Niharika Choudhary
Leaderboard
The intercept on the line y = x by the circle x2 + y2 - 2x = 0 is AB. Equation of the circle with AB as a diameter is:
A B
C D
x2 + y2 + x + y = 0 x2 + y2 - x - y = 0
x2 + y2 + x - y = 0 None of these
The intercept on the line y = x by the circle x2 + y2 - 2x = 0 is AB. Equation of the circle with AB as a diameter is:
A B
C D
x2 + y2 + x + y = 0 x2 + y2 - x - y = 0
x2 + y2 + x - y = 0 None of these
Solution :
10-04-2019-Morning Shift
The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is:
A B C D3 2
10-04-2019-Morning Shift
The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, –3), then its radius is:
A B C D3 2
Solution :
12-01-2019 - Morning Shift12-01-2019-Morning Shift
Let C1 and C2 be centres of the circles x2 + y2 -2x - 2y – 2 = 0 and x2 + y2- 6x - 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles then, area (in sq. units) of the quadrilateral PC1QC2 is : ______
A B C D8 6 9 4
12-01-2019 - Morning Shift12-01-2019-Morning Shift
Let C1 and C2 be centres of the circles x2 + y2 -2x - 2y – 2 = 0 and x2 + y2- 6x - 6y + 14 = 0 respectively. If P and Q are the points of intersection of these circles then, area (in sq. units) of the quadrilateral PC1QC2 is : ______
A B C D8 6 9 4
12-01-2019 - Morning Shift
Solution :
10-04-2019-Morning Shift
If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for..
A
B
C
D
Infinitely many values of K
No value of K.
Exactly two values of K
Exactly one value of K
10-04-2019-Morning Shift
If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for..
10-04-2019-Morning Shift
If the circles x2 + y2 + 5Kx + 2y + K = 0 and 2(x2 + y2) + 2Kx + 3y–1 = 0, (K∈R), intersect at the points P and Q, then the line 4x + 5y – K = 0 passes through P and Q, for:
A
B
C
D
Infinitely many values of K
No value of K.
Exactly two values of K
Exactly one value of K
Solution :
07-01-2020-Evening Shift
Let the tangents drawn from the origin to the circle, x2 + y2 – 8x – 4y + 16 = 0 touch it at the point A and B. Then (AB)2 is equal to:
A B C D
07-01-2020-Evening Shift
Let the tangents drawn from the origin to the circle, x2 + y2 – 8x – 4y + 16 = 0 touch it at the point A and B. Then (AB)2 is equal to:
A B C D
Solution :
12-04-2019-Morning Shift
If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :
A B C D
12-04-2019-Morning Shift
If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm) of their common chord is :
A B C D
Solution :
From origin, chords are drawn to the circle x2 + y2 - 2y = 0. The locus of the middle points of these chords is
A B
C D
x2 + y2 - y = 0 x2 + y2 - x = 0
x2 + y2 - 2x = 0 x2 + y2 - x - y = 0
From origin, chords are drawn to the circle x2 + y2 - 2y = 0. The locus of the middle points of these chords is
A B
C D
x2 + y2 - y = 0 x2 + y2 - x = 0
x2 + y2 - 2x = 0 x2 + y2 - x - y = 0
Solution :
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