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Find the equations of normal to the para...

Find the equations of normal to the parabola `y^2=4a x` at the ends of the latus rectum.

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Find the equations of normal to the parabola y^(2)=4ax at the ends of the latus rectum.

The point of intersection of the normals to the parabola y^(2)=4x at the ends of its latus rectum is

If the normals to the parabola y^(2)=4ax at the ends of the latus rectum meet the parabola at Q and Q', then QQ' is (a)10a(b)4a(c)20a(d)12a

The normal to y^(2)=4a(x-a) at the upper end of the latus rectum is

The circle described on the line joining the foci of the hyperbola (x^(2))/(16)-(y^(2))/(9) = 1 as a diameter passes through an end of the latus rectum of the parabola y^(2) = 4ax , the length of the latus rectum of the parabola is

Find the area of the triangle formed by the lines joining the vertex of the parabola y^(2) = 16x to the ends of the latus rectum.

If the normals of the parabola y^(2)=4x drawn at the end points of its latus rectum are tangents to the circle (x-3)^(2)+(y+2)^(2)=r^(2) , then the value of r^(4) is equal to

If the normals of the parabola y^(2)=4x drawn at the end points of its latus rectum are tangents to the circle (x-3)^(2)(y+2)^(2)=r^(2) then the value of r^(2) is

The triangle formed by the tangents to a parabola y^(2)=4ax at the ends of the latus rectum and the double ordinate through the focus is

A DAS GUPTA-Ellipse and Hyberbola-EXERCISE
  1. if in a hyperbola the eccentricity is sqrt3 and the distance between t...

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  2. Show that the equation x^2-2y^2-2x+8y-1=0 represents a hyperbola. Find...

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  3. Find the equations of normal to the parabola y^2=4a x at the ends of t...

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  4. Let P be a variable point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 wit...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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