Determine the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1) by following the steps below.

Question

3 years ago

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Determine the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1) by following the steps below.

Use the distance formula to determine the radius: d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot Substitute the known values into the standard form: (x – h)² + (y – k)² = r². What is the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1)? x2 + (y + 4)² = StartRoot 5 EndRoot (x – 1)² + (y + 2)² = 5 (x + 4)² + y² = 5 (x + 2)² + (y – 1)² = StartRoot 5 EndRoot

Mathematics

2 answers:

Sphinxa [80] · Answer 1 · 2022-10-22T12:21:31+03:00

Sphinxa [80]3 years ago

8 0

Answer:

its C. (x + 4)² + y² = 5

Step-by-step explanation:

edge

GaryK [48] · Answer 2 · 2022-10-22T11:12:49+03:00

Answer:

Radius length: √5

Standard Form (Equation): (x + 4)^2 + y^2 = 5

Step-by-step explanation:

First we will determine the radius;

Center: (-4, 0)

Point on Circumference: (-2, 1)

d = √(-2 - (-4))^2 + (1 - 0)^2 = √(2)^2 + (1)^2

= √4 + 1 = √5

Therefore the radius is of length √5

Now the equation of a circle is in the form ((x - h)^2 + (y - k)^2) = r^2. The center is in the form (h,k) and r is the radius. Given this our equation would be (x - (-4))^2 + (y - 0)^2 = (√5)^2, or [simplified] (x + 4)^2 + y^2 = 5.