Question

question 7 of 10
which of the following is the equation for a circle with a radius of r and center at (h, v)?
a. $(x - h)^2+(y - v)^2=r^2$
b. $(x - v)^2+(y - h)^2=r^2$
c. $h^2+v^2=r^2$
d. $(x + h)^2+(y + v)^2=r^2$

Explanation:

Step1: Recall the distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For a circle, the distance between any point \((x,y)\) on the circle and the center \((h,v)\) is the radius \(r\).

Step2: Apply the distance formula to the circle

We have \(r=\sqrt{(x - h)^2+(y - v)^2}\). Squaring both sides gives \((x - h)^2+(y - v)^2=r^2\).

Answer:

A. \((x - h)^2+(y - v)^2=r^2\)