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ABC is an isosceles triangle with its ba...

ABC is an isosceles triangle with its base BC twice its altitude. A polnt P moves within the triangle such that the square of its distance from BC is half the rectangle contained by its distances from the two sides. Show that the locus of P is an ellipse with eccentricity `sqrt(2/3)` passing through B&C.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Consider an ellipse x^2/25+y^2/9=1 with centre c and a point P on it ...

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