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  • C’ be a curve which is locus of point of intersection of lines x = 2 + m and my = 4 – m. A circle <img alt="s \equiv ( x-2 )^2 + ( y+ 1) ^2 = 25" src="https://entrancecorner.o

C’ be a curve which is locus of point of intersection of lines x = 2 + m and my = 4 – m. A circle

s \equiv ( x-2 )^2 + ( y+ 1) ^2 = 25intesects the curve C at four points P, Q, R and S. If O is

centre of the curve ‘C’, then OP^2 + OQ ^2 + OR ^2+ OS ^2 is

Option: 1

50


Option: 2

100


Option: 3

25


Option: 4

12


Answers (1)

best_answer

 

Rectangular Hyperbola -

x^{2}-y^{2}= a^{2}

- wherein

 

  

x -2 = m

               y + 1 = 4/m

          \therefore (x - 2) (y + 1) = 4

\Rightarrow XY = 4 , where \: X = x - 2, Y = y + 1

and      s \equiv ( x-2 )^2 + ( y+ 1) ^2 = 25         

\Rightarrow  X^2+ Y^2 = 25

            Curve ‘C’ & circle S both are concentric

            \         OP^2 + OQ ^2 + OR^2 + OS ^2 = 4r^2 = 4\cdot25 = 100

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Gunjita

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