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
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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
,