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Four points are such that the line joini...

Four points are such that the line joining any two points is perpendicular to the line joining other two points. If three point out of these lie on a rectangular hyperbola, then the fourth point will lie on

A

the same hyperbola

B

the conjugate hyperbola

C

one of the directrix

D

one of the asymptotes

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The correct Answer is:
A
The point are such that one of the points is the orthocenter of the triangle formed by other three points. When the vertices of a triangle lie on a rectangular hyperbola, the orthocenter also lies on the same hyperbola.
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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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