# How do you find the equation of a circle whose center of this circle is on the line 2x-5y=9 and it is tangent to both the x and y axis?

##### 2 Answers

There are

and,

#### Explanation:

Let

The Circle touches X-axis [eqn.

Similarly,

Thus, for

Since,

**Case (1) C(r,r) :=**

**Case (2) C(-r,r) :=**

**Case (3) C(-r,-r) :=**

Thus, the Centre is

**Case (4) : C(r,-r) :=**

By

Enjoy Maths.!

There are two circles in Q3 and Q4. They are given by

,

#### Explanation:

The given line makes intercepts

the second quadrant Q2 is out.

As the circle touches the axes, the equation has the form

the center

Negative a from the first is ruled out. So,

from the second and third,

a = 9/7, for the circle in Q4 and

a = 3, for the circle in Q3. .

Thus, there are two circles in Q3 and Q4. They are given by

,