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The condition that the line x cos alpha ...

The condition that the line x` cos alpha + y sin alpha =p` to be a tangent to the hyperbola ` x^(2)//a^(2) -y^(2)//b^(2) =1 ` is

A

` a^(2) cos ^(2) alpha +b^(2) sin ^(2) alpha =p^(2) `

B

` a^(2 )cos alpha -b^(2) sin ^(2) alpha =p^(2) `

C

` a^(2)sin ^(2)alpha +b^(2) cos ^(2) alpha =p^(2) `

D

`a^(2) sin ^(2) alpha +b^(2) cos ^(2)alpha =p^(2) `

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-Hyperbola -EXERCISE 1A
  1. The sum and product of the slopes of the tangents to the hyperbola 2x...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. If m1,m2 are slopes of the tangents to the hyperbola x^(2) //25 -y^...

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  16. The equations of the direcrtor cirlce of x^(2) //12 -y^(2)//8=1 is

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  17. The equations of the auxiliary circle of x^(2) //16-y^(2) //25 =1 is

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  18. The radius of the auxiliary circle of the hyperbola x^(2)//25-y^(2) /...

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  19. The tangents at a point P on x^(2)//a^(2) -y^(2)//b^(2) =1 cuts one ...

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  20. The locus of the point of interection of two tangents of the hyperbola...

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