Find an equation of the circle whose diameter has endpoints (-2,5) and (4,-3).

Question

Find an equation of the circle whose diameter has endpoints (-2,5)  and (4,-3).

563blackghost · Answer

An equation of a circle is:

$\bf{(x-h)^{2}+(y-k)^{2}=r^{2}}$

First we need to identify the center point. You are give the 2 endpoints so you would follow by midpoint formula:

$\bf\Large{(\frac{x_{1}+x_{2}}{2}},\frac{y_{1}+y_{2}}{2})$

What would be your midpoint?

surjithayer · Answer

$$if~(x_{1},y_{1})~and~(x_{2},y_{2})~are~the~extremities~of~diameter,then~eq. ~of~circle~is~$$$$=(x-x_{1})(x-x_{2})+(y-y_{1})(y-y_{2})=0$$

surjithayer · Answer

(x+2)(x-4)+(y-5)(y+3)=0
simplify it.