Question

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Answer 1

The radius of the circle is the distance between the center and a point on the circle so here it is:-

sqrt ( (5- -3)^2 + (-4-2)^2) = sqrt 100

So, using the general form (x - a)^2 + (y - b)^2 = r^2, our equation is:-

(x - 5)^2 + (y + 4)^2 = 100 answer

Answer 2

Answer:

Equation of the circle is (x - 5)² + (y + 4)² = 100

Step-by-step explanation:

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Standard equation of a circle is (x - a)² + (y - b) = r²

Where (a, b) is the center of the circle and r is the radius of the circle.

Radius of the circle r = distance between center and point lying on the circle.

$r=\sqrt{(5+3)^{2}+(-4-2)^{2}}=\sqrt{8^{2}+(-6)^{2}}$

$r=\sqrt{64+36}$

$r=\sqrt{100}=10$

Now by putting values in the standard equation of the circle.

(x - 5)² + [y - (-4)]² = 10²

(x - 5)² + (y + 4)² = 100