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Answered question

2021-11-28

Write an equation for the circle that satisfies set of conditions: endpoints of a diameter at (11, 18) and (13, -19)

Alicia Washington

Beginner2021-11-29Added 23 answers

The circle equation is

{(x + 1)}^{2} + (y + \frac{1}{2}) = \frac{1945}{4}

solution:
General equation of the circle is

{(x - a)}^{2} + {(y — b)}^{2} = r^{2}

where
(a,d)-come and r - radius
center of the circle is midpoint of (11,18) and (-13,-19)
Midpoint

= (\frac{11 - 13}{2}, \frac{18 - 19}{2}) = (- 1, \frac{- 1}{2})

center of the circle is

(- 1, \frac{- 1}{2})

Radius of the circle

= \frac{d i a m e t e r}{2}

Diameter=Distance between (11,18) and (-13,-19)

= \sqrt{{(- 13 - 11)}^{2} + {(- 19 - 18)}^{2}}

= \sqrt{576 + 1369} = \sqrt{1945}

Radius

= \frac{\sqrt{1945}}{2}

Equation of the circle:

(x - (- 1))^{2} + (y - (- \frac{1}{2}))^{2} = {(\begin{matrix} \frac{\sqrt{1945}}{2} \end{matrix})}^{2}

{(x + 1)}^{2} + {(y + \frac{1}{2})}^{2} = \frac{1945}{2}

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