Question

Find the equation for the circle with a diameter whose endpoints are (8,17) and (4, - 15).

Answer 1

Given that,

Circle with a diameter whose endpoints are (8,17) and (4, - 15).

To find the equation for the circle

we know that,

Equation of the circle is of the form,

`(x-h)^2+(y-k)^2=r^2`

where r is the radius and (h,k) is the center of the circle.

If the end points of the diameter is given, then the equation of the circle is,

`(x-x1)(x-x2)+(y-y1)(y-y2)=0`

Substitute the points we get,

`(x-8)(x-4)+(y-17)(y+15)=0`

On simplifying this we get,

`x^2-8x-4x+32+y^2-17y+15y-255=0`
`x^2+y^2-12x-2y-223=0`