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Find the Equation of a Circlewhich Touches X-axis at a Distance 5 from the Origin and Radius 6 Units. - Mathematics

Find the equation of a circle
which touches x-axis at a distance 5 from the origin and radius 6 units.

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Solution

Let (hk) be the centre of a circle with radius a.
Thus, its equation will be

\[\left( x - h \right)^2 + \left( y - k \right)^2 = a^2\]

Let the required equation of the circle be

\[\left( x - h \right)^2 + \left( y - k \right)^2 = a^2\]

It is given that the circle with radius 6 units touches the x-axis at a distance of 5 units from the origin.
∴ a = 6, h = 5

Hence, the required equation is 

\[\left( x - 5 \right)^2 + \left( y - 0 \right)^2 = 6^2\] or
\[x^2 + y^2 - 10x - 11 = 0\]
Concept: Circle - Standard Equation of a Circle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.1 | Q 7.2 | Page 21
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