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A vertical line passing through the point `(h, 0)` intersects the ellipse `x^2/4+y^2/3=1` at the points `P` and `Q`.Let the tangents to the ellipse at P and Q meet at `R`. If `Delta (h)` Area of triangle `DeltaPQR`, and `Delta_1 = max_(1/2<=h<=1)Delta(h)` and `Delta_2 = min_(1/2<=h<=1) Delta (h)` Then `8/sqrt5 Delta_1-8Delta_2`

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f1,0)a n d...

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  2. From the center C of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , perpendicul...

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  3. A vertical line passing through the point (h, 0) intersects the ellips...

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  4. A common tangent to 9x^2-16y^2 = 144 and x^2 + y^2 = 9, is

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  5. Find the equation of tangents to the curve 4x^2-9y^2=1 which are paral...

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  6. Find the equation of the locus of the middle points of the chords of ...

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  7. Find the angle between the asymptotes of the hyperbola (x^2)/(16)-(y^2...

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  8. Match the following: List - I, List - II Let y(x)=cos(3cos^(-1)x) ...

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  9. If a hyperbola passing through the origin has 3x-4y-1=0 and 4x-3y-6=0 ...

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  10. Let E1 and E2 be two ellipse whose centers are at the origin. The maj...

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  11. A triangle has its vertices on a rectangular hyperbola. Prove that the...

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  12. From any point on any directrix of the ellipse (x^2)/(a^2)+(y^2)/(b^2)...

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  13. Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+9y^2+...

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  14. A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1...

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  15. P Q and R S are two perpendicular chords of the rectangular hyperbola ...

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  16. Ois the origin & also the centre of two concentric circles having radi...

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  17. If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)...

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  18. The tangent at a point P on an ellipse intersects the major axis at T ...

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  19. If (asectheta, btantheta) and (asecphi, btanphi) be two coordinate of ...

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  20. Find the area of the triangle formed by any tangent to the hyperbola (...

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