Question

Find an equation of the circle that satisfies the stated conditions. (Give your answer in standard notation.)

Answer 1

Answer:

The equation of a circle will be:

• (x+6)² + (y - 2)² = 25

Step-by-step explanation:

We have to find the equation of the circle that satisfies the stated conditions.

• Center C(−6, 2)

• Tangent to the y-axis

We know that the equation of a circle is

(x - h)² + (y - k)² = r²

here:

• (h, k) is the center point

• r is the radius

Given that the circle is tangent to the y-axis, we just need to determine the distance between x = 0 and x = -6.

As the distance between x = 0 and x = -6 is 6. Thus, 6 will be the radius of the circle.

In other words,

• radius r = 6

Therefore, the equation of a circle is:

(x - h)² + (y - k)² = r²

(x - (-6))² + (y - 2)² = (5)²

(x+6)² + (y - 2)² = 25

Thus, the equation of a circle will be:

• (x+6)² + (y - 2)² = 25