Question

What is the equation of the circle with center (3.5) that passes through the point (-4, 10)

Answer 1

the center of the circle is (3,5)

the equation of the circle is,

(x- h )^2 + (y - K)^2 = r^2

here, h,k = coordinate of center,

r = radius of the circle.

now we find the radius,

it the distance between center (3,5) and (-4,10)

`r=\sqrt[]{(10-5)^2+(-4-3)^2}`
`\begin{gathered} r=\sqrt[]{5^2+(-7)^2} \\ r=\sqrt[]{25+49} \\ r=\sqrt[]{74} \end{gathered}`

(x - 3)^2 + (y -5)^2 = (root74)^

`\mleft(x-3\mright)^2+(y-5)^2=(\sqrt[]{74})^2`