Question

Find the equation in standard form of the circles tangent to both axes with radius 3 . Quadrant I: Quadrant It: Quadrant III: Quadrant IV:

Answer 1

Below in bold.

Explanation:

The standard form of a circle is

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

- where the centre is at (a, b) and r = radius.

Quadrant 1:

we have

(x - a)^2 + (y - b)^2 = 3^2

The circle touches the axis at (0,3) and (3.0), so

the centre is at (3, 3)

and the required equation is:

(x - 3)^2 + (y - 3)^2 = 9

Quadrant II:

The centre is at (-3, 3) so the eqation is

(x + 3)^2 + (y - 3)^2 = 9

Quadrant III:

The centre is at (-3, -3) so the eqation is

(x + 3)^2 + (y + 3)^2 = 9

Quadrant IV:

The centre is at (3, -3) so the eqation is

(x - 3)^2 + (y + 3)^2 = 9