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Find the Equation of the Circle Passing Through (0, 0) and Making Intercepts a and B on the Coordinate Axes. - Mathematics

Find the equation of the circle passing through (0, 0) and making intercepts and b on the coordinate axes.

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Solution

Let the equation of the required circle be (x – h)2 + (y – k)2 = r2.

Since the circle passes through (0, 0),

(0 – h)2 + (0 – k)2 = r2

⇒ h2 + k2 = r2

The equation of the circle now becomes (x – h)2 + (y – k)2 = h2 + k2.

It is given that the circle makes intercepts and b on the coordinate axes. This means that the circle passes through points (a, 0) and (0, b). Therefore,

(a – h)2 + (0 – k)2 = h2 + k2 … (1)

(0 – h)2 + (b – k)2 = h2 + k2 … (2)

From equation (1), we obtain

a2 – 2ah + h2 + k2 = h2 + k2

⇒ a2 – 2ah = 0

⇒ a(a – 2h) = 0

⇒ a = 0 or (a – 2h) = 0

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 11 Conic Sections
Q 13 | Page 241
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