Question

Write the equation in standard form for the circle with center (0,5) and radius 7.

Answer 1

`x^2+(y-5)^2=49`

Explanation:

Recall the formula for the graph of a circle:

`(x-h)^2+(y-k)^2=r^2\\`

Where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and r is the radius.

We are given the vertex and the length of the radius.

Substitute the values:

`(x-0)^2+(y-5)^2=7^2=\\x^2+(y-5)^2=49`

Thus, the standard form is:

`x^2+(y-5)^2=49`