Find the equation of a circle with (-1,4) and (3, –2)endpoints of its diam-aseter.

Answered: Find the equation of a circle with…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter7: Conic Sections And Quadratic Systems

Section7.CT: Chapter Test

Problem 4CT

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Question

Find the equation of a circle with (-1,4) and (3, –2)
endpoints of its diam-
as
eter.

Expert Solution

Step 1

To find the equation of a circle with $(- 1, 4)$ and $(3, - 2)$ as endpoints of its diameter.

Step 2

Since, center of circle lies on the mid-point of the diameter

let coordinates of the center be $(h, k)$

$\begin{array}{rcl} h & = & \frac{- 1 + 3}{2} \\ h & = & \frac{2}{2} \\ h & = & 1 \\ k & = & \frac{4 - 2}{2} \\ k & = & \frac{2}{2} \\ k & = & 1 \\ (h, k) & = & (1, 1) \end{array}$

Radius of the circle with center $(1, 1)$ and endpoint $(3, - 2)$ is

$\begin{array}{rcl} r & = & \sqrt{{(3 - 1)}^{2} + {(- 2 - 1)}^{2}} \\ r & = & \sqrt{{(2)}^{2} + {(- 3)}^{2}} \\ r & = & \sqrt{4 + 9} \\ r & = & \sqrt{13} \end{array}$

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