Answer:
The equation of the circle is (x + -5)² + (y + 4)² = 100
Explanation:
* Lets revise the standard form of the equation of the circle
- If the center of the circle is point (h , k) and the length of its radius is r,
then the equation of the circle is (x - h)² + (y - k)² = r² in standard form
* Now lets solve the problem
- The center of the circle is point (5 , -4)
∴ h = 5 and k = -4
∴ The equation of the circle is (x - 5)² + (y - -4)² = r²
∴ The equation of the circle is (x - 5)² + (y + 4)² = r²
- The circle passes through the point (-3 , 2)
- To find r substitute the x-coordinate and the y-coordinate of the
point in the equation of the circle
∵ Point (-3 , 2) is on the circle
∴ x = -3 and y = 2
∴ (-3 - 5)² + (2 + 4)² = r² ⇒ simplify it
∴ (-8)² + (6)² = r² ⇒ solve power 2
∴ 64 + 36 = r² ⇒ add the like terms
∴ 100 = r²
∵ The equation of the circle is (x - 5)² + (y + 4)² = r²
∴ The equation of the circle is (x - 5)² + (y + 4)² = 100
- To complete the form
∴ The equation of the circle is (x + -5)² + (y + 4)² = 100