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The tangent at any point P of a circle x...

The tangent at any point `P` of a circle `x^2 + y^2 = a^2` meets the tangent at a fixed point `A (a, 0)` in `T` and `T` is joined to `B`, the other end of the diameter through `A,` prove that the locus of the intersection of `AP` and `BT` is an ellipse whose eccentricity is `1/sqrt2`

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MOTION-ELLIPSE -Exercise - 3 | Subjective | JEE Advanced
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  2. If any two chords be drawn through two points on the major axis of an ...

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  3. The tangent at any point P of a circle x^2 + y^2 = a^2 meets the tange...

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  4. An ellipse has foci at F1(9, 20) and F2(49, 55) in the xy-plane and is...

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  5. The tangent at the point alpha on a standard ellipse meets the auxilia...

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  6. Find the equations of the lines with equal intercepts on the axes & wh...

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  7. If a tangent having a slope of -4/3 to the ellipse x^2/18 + y^2/32 = 1...

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  8. Let d be the perpendicular distance from the centre of the ellipse x^2...

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

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  10. If the tangent at any point of an ellipse x^2/a^2 + y^2/b^2 =1 makes a...

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  11. Common tangents are drawn to the parabola y^2 = 4x & the ellipse 3x^2 ...

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  12. P & Q are the corresponding points on a standard ellipse & its auxilia...

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  13. A tangent to the ellipse x^2/a^2 +y^2/b^2 =1 touches at the point P on...

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  14. If the normal at the point P( theta) to the ellipse (x^(2))/(14)...

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  15. PG is the normal to a standard ellipse at P, G being on the major axis...

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  16. Suppose xa n dy are real numbers and that x^2+9y^2-4x+6y+4=0 . Then th...

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  17. ABC is an isosceles triangle with its base BC twice its altitude. A po...

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  18. A circle intersects an ellipse x^2/a^2+y^2/b^2=1 precisely at three po...

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  19. Given the equation of the ellipse (x-3)^2/(16)+(y-4)^2/(49)=1 a parabo...

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  20. Consider the parabola y^2 =4x and the ellipse 2x^2 + y^2 =6, intersect...

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