Question

Center:(4,-10)

Point of circle: (12, -10)

how do you use this information to write an equation?

Answer 1

(x – 4)^2 + (y +10)^2 = 64

Explanation:

Recall that the formula for a circle is: (x – h)^2 + (y – k)^2 = r^2

1. Find the Radius (r): Luckily, we can count the distance since the coordinates have the same y-value. 12 - 4 = 8. So, r^2 = 8^2 = 64

2. Find h and k. These are the x and y coordinates of the center of the circle. So, h = 4, k = -10

3. Substitute the values in the equation:

(x – 4)^2 + (y – (-10))^2 = 8^2

(x – 4)^2 + (y +10)^2 = 64

Answer 2

(x -4)² +(y +10)² = 64

Explanation:

Given a circle through point (12, -10) with center (4, -10), you want its equation.

Equation

The equation of a circle with center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

Application

You are given the center (h, k) = (4, -10). You only need to know the radius to finish the equation. That will be the value of r that makes the equation true at the given point:

(x -4)² + (y +10)² = r²

(12 -4) + (-10 +10)² = r² . . . . . . with (x, y) = (12, -10), the point on the circle

8² + 0 = r²

The equation of the circle is (x -4)² +(y +10)² = 64.

__

Additional comment

The equation of a circle is essentially a statement of the distance formula. It is telling you that the circle consists of all points that are distance r from the center.

<95141404393>