Question

The point (4,7) lies on the circle centered at (-3,-2), how do you find the equation of the circle in standard form?

Answer 1

`(x + 3 )^2 + (y + 2)^2 = 130`

Explanation:

the equation of a circle in standard form is :

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

where (a , b ) is the centre and r , the radius

In this question the centre is given but require to find r

the distance from the centre to a point on the circle is radius.

calculate r using `color(blue)(" distance formula ")`

which is : `r = sqrt( (x_2 - x_1 )^2 + (y_2 - y_1 )^2)`

using `(x_1 , y_1 ) = (-3,-2))color(black)(" and") (x_2 , y_2) = (4,7)`

then `r =sqrt(4-(-3)^2+(7-(-2)^2)) =sqrt(49+81) =sqrt130`

circle equation using centre =(a , b ) = (-3 , -2) , r `=sqrt130`

`rArr (x+3)^2 +(y+2)^2 = 130`