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?
The Circle touches X-axis [eqn.
Case (1) C(r,r) :=
Case (2) C(-r,r) :=
Case (3) C(-r,-r) :=
Thus, the Centre is
Case (4) : C(r,-r) :=
There are two circles in Q3 and Q4. They are given by
The given line makes intercepts
the second quadrant Q2 is out.
As the circle touches the axes, the equation has the form
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