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If S=0 is the equation of the hyperbola ...

If `S=0` is the equation of the hyperbola `x^2+4x y+3y^2-4x+2y+1=0` , then the value of `k` for which `S+K=0` represents its asymptotes is

A

20

B

`-16`

C

`-22`

D

18

Text Solution

Verified by Experts

The correct Answer is:
C
For the equation `S+K=0` to represent a pair of lines,
`|(1,2,-2),(2,3,1),(-2,1,1+K)|=0`
`"or "K=-22`
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CENGAGE PUBLICATION-HYPERBOLA-EXERCISES
  1. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

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  2. Let any double ordinate P N P ' of the hyperbola (x^2)/(25)-(y^2)/(16)...

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  3. For hyperbola whose center is at (1, 2) and the asymptotes are paralle...

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  4. The asymptotes of the hyperbola (x^(2))/(a(1)^(2))-(y^(2))/(b(1)^(2))=...

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  5. If S=0 is the equation of the hyperbola x^2+4x y+3y^2-4x+2y+1=0 , then...

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  6. If two distinct tangents can be drawn from the point (alpha, alpha+1) ...

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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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  20. Let C be a curve which is the locus of the point of intersection of li...

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