Question

Determine the equation of the circle graphed below.

10
-10 -8 -6
-4
-2
8
6
4
N
N
+
69
O
2
6
8 10

Answer 1

`\implies x^2+y^2-4x -6y+9=0`

Explanation:

Circle is touching y-axis at point (0, 3) and is centered at (2, 3)

-> h = 2, k = 3 & r = 2 units (If a circle touches y -axis then x coordinate of the center will be it's radius)

Equation of circle in standard form is given as:

`(x-h)^2 +(y-k)^2 =r^2`

Plugging the values of h, k and r in the above equation, we find:

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

`\implies x^2-4x +4+y^2-6y+9=4`

`\implies x^2+y^2-4x -6y+4+9=4`

`\implies x^2+y^2-4x -6y+9=0`

This is the required equation of the circle.