Question

Write an equation of a circle whose center is at (-3,5) and goes through the point (4,-2). Write the equation in standard and general form

Answer 1

`{(x + 3)}^(2) + {(y - 4)}^(2)=98`

Explanation:

The standard form equation of a circle is given as:

`{(x - a)}^(2) + {(y - b)}^(2) = {r}^(2)`

Where (a,b) is the center and r is the radius.

We need to use the distance formula to obtain the radius.

`r = √((x_2-x_1)^2 +(y_2-y_1)^2)`

We substitute the center (-3,5) and (4,-2) to get:

`r = √((4- - 3)^2 +( - 2 - 5)^2)`

`r = √((7)^2 +( - 7)^2)`

`r = √(98)`

We now substitute the center and radius to get:

`{(x - - 3)}^(2) + {(y - 4)}^(2) = { (√(98) })^(2)`

The standard form equation is;

`{(x + 3)}^(2) + {(y - 4)}^(2)=98`