Find the equation of a circle that has its center at (-4, 3) and has a radius of 5.

Solution:

Given: Center(h, k) = (-4, 3) and radius(r) = 5.

We know that the general equation of circle with center (h, k) and radius with r is (x - h)² + (y - k)² = r²

Substitute the values of h, k, r in the standard form, we get

⇒ (x - (-4))² + (y - 3)² = 5²

⇒ (x + 4)² + (y - 3)² = 25.

We know that algebraic identites (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b²

⇒ x² + 8x +16 + y² - 6y + 9 = 25

⇒ x² + y² + 8x - 6y = 0

Therefore, the equation of a circle that has its center (-4, 3) and has a radius of 5 is (x + 4)² + (y - 3)² = 25.

Find the equation of a circle that has its center at (-4, 3) and has a radius of 5.

Summary:

The equation of a circle that has its center at (-4, 3) and has a radius of 5 is (x + 4)² + (y - 3)² = 25.