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If a tangent to the ellipse `x^2/a^2+y^2/b^2=1`, whose centre is C, meets the major and the minor axes at P and Q respectively then `a^2/(CP^2)+b^2/(CQ^2)` is equal to

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If the normal at any point P on the ellipse x^2/a^2 + y^2/b^2 = 1 cuts the major and minor axes in L and M respectively and if C is the centre, then a^2 CL^2 + b^2 CM^2 = (A) (a-b) (B) (a^2 - b^2) (C) (a+b) (D) (a^2 + b^2)

If the normal at any point P of the ellipse x^2/a^2 + y^2/b^2 = 1 meets the major and minor axes at G and E respectively, and if CF is perpendicular upon this normal from the centre C of the ellipse, show that PF.PG=b^2 and PF.PE=a^2 .

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A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. Let P be a variable point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 wit...

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  2. The number of maximum normals that can be drawn from any point to an e...

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  3. If a tangent to the ellipse x^2/a^2+y^2/b^2=1, whose centre is C, me...

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  4. Find the length of the chord of the ellipse x^2/25+y^2/16=1, whose mid...

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  5. If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b...

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  6. Show that 3x^(2) - 3y^(2) - 18x + 12y + 2 = 0 represents a rectangular...

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  7. The point P on the ellipse 4x^2+9y^2=36 is such that the are of the P...

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  8. If the tangent and normal to a rectangular hyperbola cut off intercept...

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  9. The equation 14x^2 - 4xy+ 11y^2 - 44x - 58y + 71 = 0 represents

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  10. If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(...

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  11. Find the eccentric angle of a point on the ellipse x^2 + 3y^2 = 6 at a...

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  12. Which of the following is an exterior point of the ellipse 16x^2+9y^2-...

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  13. The line 3x+5y=k touches the ellipse 16x^(2)+25y^(2)=400 ,if k is

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  14. Find the equaiton of the tangents to the hyperbola x^2 - 2y^2 = 18 whi...

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  15. A point on the ellipse x^2+3y^2=37 where the normal is parallel to the...

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  16. if the ordinate of the point of contact be 2 then the equation of the ...

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  17. A tangent to the ellipse 16x^2 + 9y^2 = 144 making equal intercepts o...

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  18. If the tangent to the ellipse x^2 +4y^2=16 at the point 0 sanormal to ...

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  19. An ellipse having foci (3,1) and (1, 1) passes through the point (1, 3...

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  20. If P & Q are the ends of a pair of conjugate diameters & C is the cent...

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