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Tangents are drawn from the point `(alpha, beta)` to the hyperbola `3x^(2)-2y^(2)=6` and are inclined at angle `theta` and `phi` to the x-axis. If `tan theta*tan phi=2`, then the value `2alpha^(2)-beta^(2)` is ____________.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
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  2. If the hyperbola x^2-y^2=4 is rotated by 45^0 in the anticlockwise dir...

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  3. Find the point on the hyperbola x^2/24 - y^2/18 = 1 which is nearest t...

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  4. The number of possible tangents which can be drawn to the curve 4x^2-9...

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  5. If values of a, for which the line y=ax+2sqrt(5) touches the hyperbola...

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  6. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

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  7. The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the...

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  8. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

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  9. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

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  10. The locus of a point whose chord of contact with respect to the circle...

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  11. Locus of the feet of the perpendiculars drawn from either foci on a va...

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

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  13. If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4, then the po...

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  14. Which of the following is independent of alpha in the hyperbola (0 ...

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  15. Consider the graphs of y = Ax^2 and y^2 + 3 = x^2 + 4y, where A is a p...

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  16. Tangents are drawn from the point (alpha, beta) to the hyperbola 3x^(2...

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  17. The eccentricity of the hyperbola |sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+...

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  18. If y=m x+c is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, havi...

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  19. A(-2, 0) and B(2,0) are two fixed points and P 1s a point such that PA...

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  20. Statement 1 : Given the base B C of the triangle and the radius ratio ...

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