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Write the Equation of the Unit Circle Concentric with X2 + Y2 − 8x + 4y − 8 = 0. - Mathematics

Write the equation of the unit circle concentric with x2 + y2 − 8x + 4y − 8 = 0.

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Solution

The centre of the circle x2 + y2 − 8x + 4y − 8 = 0 is (4, −2).
The radius of the unit circle is 1.
∴ Required equation of circle:

\[\left( x - 4 \right)^2 + \left( y + 2 \right)^2 = 1\],

\[\Rightarrow\] \[x^2 + y^2 - 8x + 4y + 19 = 0\]

Concept: Circle - Standard Equation of a Circle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Q 5 | Page 38
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