What will be the equation of the circle with a center at (–4, 9) and a diameter of 10 units?

Solution:

We can make use of the standard form of the equation of the circle. Go through the step-by-step procedure to get the final equation of the circle.

Given, center coordinates = (-4, 9) and diameter = 10 units.

radius = diameter / 2 = 5 units

Using the standard equation of the circle, which is :

(x - h)² + (y - k)² = r² , where:

h = x coordinate of the center

k = y coordinate of the center

r = radius of the circle.

Thus on substituting the value of h, k, and r in the standard equation, we get:

(x + 4)² + (y - 9)² = 5²

⇒ (x + 4)² + (y - 9)² = 25

Thus the equation of the circle, can be given as  (x + 4)² + (y - 9)² = 25.

⇒ x² +y² +8x-18y = 25 -16 -81

⇒ x² +y² +8x-18y =-72

What will be the equation of the circle with a center at (–4, 9) and a diameter of 10 units?

Summary:

The equation of the circle, can be given as  (x + 4)² + (y - 9)² = 25 or x² +y² +8x-18y =-72