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P(theta) and D(pi/2+theta) are two point...

`P(theta)` and `D(pi/2+theta)` are two points on the ellipse `x^2/a^2+y^2/b^2=1`. Show that the locus of the point of intersection of tangents at P and Q to the ellipse is `x^2/a^2+y^2/b^2=2`

A

`x^(2)//a^(2)+y^(2)//b^(2)=1//a`

B

`x^(2)//a^(2)+y^(2)//b^(2)=1//b`

C

`x^(2)//a^(2)+y^(2)//b^(2)=1//2`

D

`x^(2)//a^(2)+y^(2)//b^(2)=1//6`

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DIPTI PUBLICATION ( AP EAMET)-ELLIPSE-EXERCISE 1A
  1. The parametric representation (2+t^(2),2t+1) represents

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  2. The points on the ellipse 2x^(2)+3y^(2)=6 whose eccentric angles diffe...

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  3. The equation of the tangent at a point theta=3pi//4 to the ellipse x^(...

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  4. The equation of the normal to the ellipse x^(2)//16+y^(2)//9=1 at the...

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  5. If x/a+y/b=sqrt(2) touches the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1, then...

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  6. The distance of a point on the ellipse x^(2)//6+y^(2)//2=1 from the ce...

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  7. The eccentric angles of the extremities of latusrecta of the ellipse x...

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  8. The tangent and normal to the ellipse 4x^(2)+9y^(2)=36 at a point P on...

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  9. If alpha and beta are the eccentric angles of the ends of a focal chor...

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  10. The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))...

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  11. The locus of the foot of perpandicular drawn from the centre of the e...

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  12. If P is a point on the ellipse of eccentricity e and A, A 1 are the ve...

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  13. P(theta) and D(pi/2+theta) are two points on the ellipse x^2/a^2+y^2/b...

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  14. P(theta) and D(pi/2+theta) are two points on the ellipse x^2/a^2+y^2/b...

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

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  16. The condition that the line lx + my + n= 0 to be a normal to the ellip...

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  17. The normal at a poitn P( theta) on the ellipse 5x^(2) +14y^(2) =70 ...

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  18. If the normal at theta on the hyperbola x^(2)//a^(2)-y^(2)//b^(2)=1 me...

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  19. The tangent at a point P(acos theta,bsin theta) on the ellipse (x^(2))...

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  20. The tangent at 'p' on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 cu...

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