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Suppose the circle having equation x^2+y...

Suppose the circle having equation `x^2+y^2=3` intersects the rectangular hyperbola `x y=1` at points `A ,B ,C ,a n dDdot` The equation `x^2+y^2-3+lambda(x y-1)=0,lambda in R ,` represents.

A

a pair of lines through the origin for `lambda=-3`

B

an ellipse through A, B, C and D for `lambda=-3`

C

a parabola through A, B, C and D for `lambda=-3`

D

a circle for any `lambda in R`

Text Solution

Verified by Experts

The correct Answer is:
A
For `lambda=-3`, the equation becomes
`x^(2)+y^(2)-3xy=0`
which represents a pair of lines through the origin.
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  7. A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12 x...

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  8. From any point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , tangents a...

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  9. The combined equation of the asymptotes of the hyperbola 2x^2 + 5xy + ...

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  10. The asymptotes of the hyperbola x y=h x+k y are (1)x-k=0 and y-h=0 (2...

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  11. The center of a rectangular hyperbola lies on the line y=2xdot If one ...

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  12. The equation of a rectangular hyperbola whose asymptotes are x=3 and y...

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  13. If tangents O Q and O R are dawn to variable circles having radius r a...

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  14. Four points are such that the line joining any two points is perpendic...

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  15. If S1a n dS2 are the foci of the hyperbola whose length of the transve...

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  16. Suppose the circle having equation x^2+y^2=3 intersects the rectangula...

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  17. The equation to the chord joining two points (x1,y1)a n d(x2,y2) on th...

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  18. The locus of the foot of the perpendicular from the center of the hy...

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  19. The curve xy = c(c > 0) and the circle x^2 +y^2=1 touch at two points,...

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