Question

Find the equation of a circle with a center at (-1, 5) and a point on the circle is (4, 4).

Answer 1

`(x +1)^2+(y-5)^2=26`

Explanation:

Use the distance formula to find the radius using the center (-1,5) and the point (4,4).

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

This implies that;

`r = \sqrt{(4 - - 1)^(2) + ( {4 - 5)}^(2) }`

`r = \sqrt{ {5}^(2) + {( - 1)}^(2) }`

`r = √(26)`

We use the formula:

`(x- - 1)^2+(y-5)^2=( √(26)) ^2`

`(x + 1)^2+(y-5)^2=26`

The required equation is

`(x + 1)^2+(y-5)^2=26`