Question

A circle is centered at the point (5, -4) and passes through the point (-3, 2). The equation of this circle is (x + )2 + (y + )2 = . Reset

Answer 1

Answer:

$(x-5)^{2}+(y+4)^{2}=100$

Explanation:

We have been given the center of the circle as (5, -4) and a point on the circumference as (-3, 2). We first determine the radius of the circle. The radius is the distance from the center to any point on the circumference. Using the distance formula, we have;

$radius=\sqrt{(5--3)^{2}+(-4-2)^{2}}\\radius=\sqrt{64+36}=10$

The radius of the circle is thus 10 units.

The equation of a circle with center (a,b) and radius r units is given as;

$(x-a)^{2}+(y-b)^{2}=r^{2}$

Plugging in the values given we have;

$(x-5)^{2}+(y+4)^{2}=100$