Question

Find the center and radius of the circle whose diameter has an endpoint at (-3, -4) and the origin.

Answer 1

Given end points of diameter,

(x1,y1)=(-3,-4)

(x2,y2)=(0,0)

Now,

the equation of circle is,

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

or, (x+3)(x-0)+(y+4)(y-0)=0

or, x^2 +3x +y^2 +4y =0

or, x^2 +y^2 +3x + 4y=0

which is in the form of x^2 +y^2 +2gx +2fy + c=0

where,

g=3/2

h=2

c=0

Now,

$radius(r) = \sqrt{ {g}^{2} + {f}^{2} - c } \\ = \sqrt{ \frac{ {3}^{2} }{ {2}^{2} } + {2}^{2} - 0 } \\ = \sqrt{ \frac{9}{4} + 4} \\ = \sqrt{ \frac{25}{4} } \\ = \frac{5}{2}$