Question

What is the standard form of the equation for this circle?

A. ( (x - 4)² + (y + 5)² = 5.5 )

B. ( (x - 4)² + (y + 5)² = 30.25 )

C. ( (x + 4)² + (y - 5)² = 30.25 )

D. ( (x + 4)² + (y + 5)² = 11 )

E. ( (x + 4)² + (y - 5)² = 5.5 )

Answer 1

The standard form of the equation for a circle given in the options is B. ( (x - 4)² + (y + 5)² = 30.25 ), which represents a circle with a center at (4, -5) and a radius of 5.5.

Step-by-step explanation:

The question asks about the standard form of the equation for a circle. The standard form for a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To find the correct option, we must look for an equation that matches this form.

Option B, ((x - 4)² + (y + 5)² = 30.25), matches the standard form with the center at (4, -5) and a radius of sqrt(30.25), which is 5.5. As none of the other options match the correct center and radius combination, Option B is the equation in standard form for the given circle.

Therefore, the correct answer is B. ( (x - 4)² + (y + 5)² = 30.25 ) as this represents a circle with a center at (4, -5) and a radius of 5.5.