Question

Instructions: Given the equation of the circle, find the center and radius.

Equation: (x−8)2+(y−7)2=25

Answer 1

Center: (8, 7)

Radius: 5 units

Explanation:

(x - 8)^2 + (y - 7)^2 = 25 is the standard form of an equation of a circle, whose general equation is given by:

(x - h)^2 + (y - k)^2 = r^2, where:

• (h, k) are the coordinates of the circle's center,
• and r is the radius.

Finding the coordinates of the center:

Therefore, the coordinates of the center are (8, 7).

Finding the radius:

Since the radius in the standard form is squared, we take its square root to find the radius of the circle:

Radius = √25

Radius = 5

Therefore, the radius of the circle is 5 units.