Type the correct answer in each box. 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 =

Question

asked Aug 27, 2023 81.8k views

1 Answer

Mirageglobe · Answer 1 · 2023-09-01T21:49:57+0000

Answer:

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

Explanation:

Equation of a circle

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

where:

Given:

Substitute the given values into the circle equation and solve for r:

$\implies r^2=(-3-5)^2+(2-(-4))^2$

$\implies r^2=(-8)^2+(6)^2$

$\implies r^2=64+36$

$\implies r^2=100$

$\implies r=√(100)$

$\implies r=10$

Substitute the given center and the found value of r into the circle equation to create the equation of the circle:

$\implies (x-5)^2+(y-(-4))^2=10^2$

$\implies (x-5)^2+(y+4)^2=100$