What is the equation of a circle with center at (3, -2) and radius 4? (2023)

₹0.0

Question: What is the equation of a circle with center at (3, -2) and radius 4? (2023)

Options:

Correct Answer: (x-3)² + (y+2)² = 16

Exam Year: 2023

Solution:

The standard equation of a circle is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=4. Thus, (x-3)² + (y+2)² = 16.

What is the equation of a circle with center at (3, -2) and radius 4? (2023)

What is the equation of a circle with center at (3, -2) and radius 4? (2023)

Step 1: Identify the center of the circle. The center is given as (3, -2). Here, h = 3 and k = -2.
Step 2: Identify the radius of the circle. The radius is given as 4.
Step 3: Recall the standard equation of a circle, which is (x - h)² + (y - k)² = r².
Step 4: Substitute the values of h, k, and r into the equation. This means replacing h with 3, k with -2, and r with 4.
Step 5: The equation becomes (x - 3)² + (y - (-2))² = 4².
Step 6: Simplify the equation. Since y - (-2) is the same as y + 2, the equation is (x - 3)² + (y + 2)² = 16.

No concepts available.