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For the hyperbola (x^(2))/( cos ^(2) al...

For the hyperbola ` (x^(2))/( cos ^(2) alpha ) -(y^(2))/(sin^(2) alpha ) =1` ,which of the following remains constant when `alpha ` varies?

A

Eccentricity

B

Directrix

C

Abscissae of vertices

D

Abscissae of foci

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-Hyperbola -EXERCISE 1A
  1. If the foci of the ellips (x^(2))/( 25)+ ( y^(2))/( 16) =1 and the hy...

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  2. The foci of the ellips (x^(2))/( 16) +(y^(2))/( b^(2) ) =1 and the h...

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  3. For the hyperbola (x^(2))/( cos ^(2) alpha ) -(y^(2))/(sin^(2) alpha ...

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  4. A hyperbola passes through a focus of the ellips (x^(2))/(169) +(y^(2...

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  5. The equation of the tangent to the hyperbola 3x^(2) -2y^(2) =10 at(2,...

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  6. The equation of the normal to the hyperbola x^(2) -4y ^(2) =5 at (3,-...

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  7. The sum and product of the slopes of the tangents to the hyperbola 2x...

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  8. The condition that the line y = mx+c may be a tangent to the hyperbo...

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  9. The condition that the line x cos alpha + y sin alpha =p to be a tange...

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  10. The condition that the line (x)/(p) +(y)/( q) =1 to be a tangent to ...

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  11. In the line 3x-y= k is a tangent to the hyperbola 3x^(2) -y^(2) =3 ...

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  12. The values of m for which the line y =mx +2 become a tangent to the hy...

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  13. The equation of the tangents to the hyperbola 3x^(2) -4y^(2) =12 whic...

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  14. The equations of the tangents to the hyperbola 2x^(2) -3y^(2) =6 whic...

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  15. The equations of the tangents to the hyperbola 9x^(2) -16y^(2) =144 ...

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  16. The equations of the tangents to the hyperbola 3x^(2) -4y^(2) =12 whi...

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  17. The equations of the tangents to the hyperbola 4x^(2) -5y^(2) =20 wh...

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  18. Equation of one of the tangents passing through (2, 8) to the hyperbol...

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  19. The point of contact of 5x+6y+1=0 to the hyperbola 2x^(2)-3y^(2)=2 is

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  20. The number of tangents to x^(2)//9 -y^(2) //4=1 through (6,2) is

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