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How to solve this problem- - Two-dimensional Coordinate Geometry - BITSAT

If (4,-2) is a point on the circle x^{2}+y^{2}+2gx+2fy+c=0

which is concentric to  x^{2}+y^{2}-2x+4y+20=0\:then\:value\:of C\: is

  • Option 1)

    -4

  • Option 2)

    0

  • Option 3)

    4

  • Option 4)

    1

 
Answers (2)
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Since both circles are concentric so coordinate of their centre is (1,-2)=(-g ,-f) 

Put the given value of (x,y)=(4,-2) and "g and f "

4^2+(-2)^2+2×(-1)×4+2×2×(-2)+C=0

=> C= -4

Thank you 

 

 

General form of a circle -

x^{2}+y^{2}+2gx+2fy+c= 0
 

- wherein

centre = \left ( -g,-f \right )

radius = \sqrt{g^{2}+f^{2}-c}

 

 For concentric, g=1, f=2

so; x^{2}+y^{2}-2x+4y+c=0

Satisfying by (4, -2);

16+4-8-8+c=0

\Rightarrow c=-4


Option 1)

-4

This solution is correct

Option 2)

0

This solution is incorrect

Option 3)

4

This solution is incorrect

Option 4)

1

This solution is incorrect

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