Question

Write the equation of a circle with a center at (-1, -4) that passes through the point (-1,-1)

Answer 1

Equation of the circle :

`(x+ 1)^2 + (y+4)^2 = 9`

Explanation:

Equation of a circle with centre (a, b) and radius ,r :

`(x - a)^2 + (y-b)^2 = r^2` ------(1)

Here a = -1, b = -4

find radius:

Since the circle passes through (-1, -1) , the radius is the distance between the centre and the point.

`distance, r = √((-1 -(-1))^2 +(-4 -(-1))^2 )`

`= √(9) = 3`

Substitute the values in (1) :

`(x - (-1))^2 + (y-(-4))^2 = 3^2\\\\(x+ 1)^2 + (y+4)^2 = 9`