A circle is represented by the equation below: (x + 8)² + (y - 3)² = 100. Which statement is true?
(i) The circle is centered at (-8, 3) and has a radius of 20.
(ii) The circle is centered at (8, -3) and has a diameter of 20.
(iii) The circle is centered at (8, -3) and has a radius of 20.
(iv)The circle is centered at (-8, 3) and has a diameter of 20.

Solution:

Given: Equation is (x + 8)² + (y − 3)² = 100 --- (A)

Comparing equation (A) w.r.t. the general equation of a circle is (x-h)²+ (y-k)² = r² centred at (h, k) and radius 'r' we get ,

Centre of the circle = (h, k) = (-8, 3) and r = 10 ⇒ d = 20

∴ Option (iv) is the true statement.

A circle is represented by the equation below: (x + 8)² + (y - 3)² = 100. Which statement is true?
(i) The circle is centered at (-8, 3) and has a radius of 20.
(ii) The circle is centered at (8, -3) and has a diameter of 20.
(iii) The circle is centered at (8, -3) and has a radius of 20.
(iv)The circle is centered at (-8, 3) and has a diameter of 20.

Summary:

For a circle represented by the equation: (x + 8)² + (y - 3)² = 100, the circle is centered at (-8, 3) and has a diameter of 20.