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

##### 1 Answer

Feb 1, 2016

# (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 #