Distance and Midpoint Formulas; Circles

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October 21, 2019

Distance and Midpoint Formulas; Circles

Objectives:• Find the distance between two points.• Find the midpoint of a line segment.• Write the standard form of a circle’s equation.• Give the center and radius of a circle whose equation is in standard form.

• Convert the general form of a circle’s equation to standard form.

Distance and Midpoint Formulas; Circles

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October 21, 2019

Distance and Midpoint Formulas; Circles

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October 21, 2019

Distance and Midpoint Formulas; Circles

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October 21, 2019

Distance and Midpoint Formulas; Circles

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October 21, 2019

Distance and Midpoint Formulas; Circles

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October 21, 2019

(x ­ ­2)2 + (y ­ 3)2 = (4)2

(x + 2)2 + (y ­ 3)2 = 16

Distance and Midpoint Formulas; Circles

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October 21, 2019

Center: (­3, 1) Radius = 2

Domain: h ­ r, h + r

Range: k ­ r, k + r

Domain: ­3 ­ 2 , ­3 + 2

[­5, ­1]

Range: 1 ­ 2, 1 + 2

[­1, 3]

Distance and Midpoint Formulas; Circles

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October 21, 2019

x2 + y2 + 4x ­ 6y ­ 23 = 0

x2 + 4x + y2 ­ 6y = 23

x2 + 4x + 4+ y2 ­ 6y + 9 = 23 + 4 + 9

(x + 2)2 + (y ­ 3)2 = 36

Center: (­2, 3) Radius: 6

Distance and Midpoint Formulas; Circles

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October 21, 2019