Question

there is a circle with center (4,5). the point (8,5) is also on the circle. find the equation of the circle and put it in standard form.

Answer 1

The equation of a circle with center at (4,5) and passing through the point (8,5) is (x - 4)^2 + (y - 5)^2 = 16.

Step-by-step explanation:

To find the equation of a circle with center at (4,5) and passing through the point (8,5), we need to use the standard form of the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is its radius. Since the point (8,5) lies on the circle, it is the same distance from the center as any other point on the circle. This distance is the radius of the circle.

First, let's calculate the radius:

• Distance between the center (4,5) and the point on the circle (8,5) is the difference in the x-values because the y-values are the same.
• The radius r = 8 - 4 = 4 units.

Now, we can plug the center coordinates and the radius into the standard form equation:

• (x - 4)^2 + (y - 5)^2 = 4^2
• This simplifies to (x - 4)^2 + (y - 5)^2 = 16.

This is the standard form equation of the circle with the given center and point.