We will learn how to find the equation of a circle touches both xaxis and yaxis.
The equation of a circle with centre at (h, k) and radius equal to a, is (x  h)\(^{2}\) + (y  k)\(^{2}\) = a\(^{2}\).
When the circle touches both xaxis and yaxis i.e., h = k = a.
Then the equation (x  h)\(^{2}\) + (y  k)\(^{2}\) = a\(^{2}\) becomes (x  a)\(^{2}\) + (y  a)\(^{2}\) = a\(^{2}\)
If a circle touches both the coordinate axes then the abscissa as well as ordinate of the centre will be equal to the radius of the circle. Hence, the equation of the circle will be of the form:
(x  a)\(^{2}\) + (y  a)\(^{2}\) = a\(^{2}\)
⇒ x\(^{2}\) + y\(^{2}\)  2ax  2ay + a\(^{2}\) = 0
Solved example on the central form of the equation of a circle touches both xaxis and yaxis:
1. Find the equation of a circle whose radius is 4 units and touches both xaxis and yaxis.
Solution:
Radius of the circle = 4 units.
Since, the circle touches both xaxis and yaxis the centre of the circle is (4, 4).
The required equation of the circle whose radius is 4 units and touches both xaxis and yaxis is
(x  4)\(^{2}\) + (y  4)\(^{2}\) = 4\(^{2}\)
⇒ x\(^{2}\)  8x + 16 + y\(^{2}\)  8y + 16 = 16
⇒ x\(^{2}\)  8x  8y + 16 = 0
2. Find the equation of a circle whose radius is 8 units and touches both xaxis and yaxis.
Solution:
Radius of the circle = 8 units.
Since, the circle touches both xaxis and yaxis the centre of the circle is (8, 8).
The required equation of the circle whose radius is 8 units and touches both xaxis and yaxis is
(x  8)\(^{2}\) + (y  8)\(^{2}\) = 8\(^{2}\)
⇒ x\(^{2}\)  16x + 64 + y\(^{2}\)  16y + 64 = 64
⇒ x\(^{2}\) + y\(^{2}\)  16x  16y + 64 = 0
11 and 12 Grade Math
From Circle Touches both xaxis and yaxis to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.