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Lemur [1.5K]
2 years ago
9

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]2 years ago
8 0

Answer:

its C. (x + 4)² + y² = 5

Step-by-step explanation:

edge

GaryK [48]2 years ago
6 0

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.

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The only error you made is on problem 3. Everything else is correct. Nice work.

-------------------------------------------------------

Here is how to solve problem 3

Plug x = 1 into the equation and solve for y

-3x + y = 1

-3*1 + y = 1 ... replace x with 1

-3 + y = 1

y - 3 = 1

y - 3 + 3 = 1 + 3 .... add 3 to both sides

y = 4

<h3>The answer is 4</h3>

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Verifying the answer:

Plug (x,y) = (1,4) into the equation. Both sides should be the same number after simplifying both sides.

-3x + y = 1

-3*1 + 4 = 1 ..... replace x with 1; replace y with 4

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1 = 1

The answer is confirmed.

If you were to graph -3x + y = 1, which is equivalent to y = 3x+1, you'll find that the point (1,4) is on this line.

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Step-by-step explanation:

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