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If (−3, 2) Lies on the Circle X2 + Y2 + 2gx + 2fy + C = 0 Which is Concentric with the Circle X2 + Y2 + 6x + 8y − 5 = 0, Then C = - Mathematics

MCQ

If (−3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0 which is concentric with the circle x2 + y2 + 6x + 8y − 5 = 0, then c =

Options

  • 11

  • -11

  • 24

  • none of these

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Solution

  −11

The centre of the circle x2 + y2 + 6x + 8y − 5 = 0 is (−3, −4).
The circle x2 + y2 + 2gx + 2fy + c = 0 is concentric with the circle x2 + y2 + 6x + 8y − 5 = 0.
Thus, the centre of x2 + y2 + 2gx + 2fy + c = 0 is (−3, −4).

\[\therefore g = 3, f = 4\]

Also, it is given that (−3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0.

\[\left( - 3 \right)^2 + 2^2 + 2\left( 3 \right)\left( - 3 \right) + 2\left( 4 \right)\left( 2 \right) + c = 0\]

\[\Rightarrow 9 + 4 - 18 + 16 + c = 0\]

\[ \Rightarrow c = - 11\]

Concept: Circle - Standard Equation of a Circle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Q 22 | Page 40
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