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If two points are taken on the minor axi...

If two points are taken on the minor axis of an ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is `2a^2dot`

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (x1, y...

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  2. Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 2).

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  3. If two points are taken on the minor axis of an ellipse (x^2)/(a^2)...

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  4. If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts e...

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  5. Find the slope of a common tangent to the ellipse (x^2)/(a^2)+(y^2)/(b...

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  6. If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^...

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  7. If F1 and F2 are the feet of the perpendiculars from the foci S1a ...

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  8. If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 m...

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  9. Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=...

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  10. A tangent having slope of -4/3 to the ellipse (x^2)/(18)+(y^2)/(32)=...

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  11. If the tangent to the ellipse x^2+2y^2=1 at point P(1/(sqrt(2)),1/2) m...

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  12. Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the...

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  13. Find the locus of the middle points of all chords of (x^2)/4+(y^2)/...

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  14. Tangents P Qa n dP R are drawn at the extremities of the chord of th...

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  15. If the chords of contact of tangents from two poinst (x1, y1) and ...

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  16. From the point A(4,3), tangent are drawn to the ellipse (x^2)/(16)...

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  17. An ellipse is drawn with major and minor axis of length 10 and 8 resp...

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  18. Find the foci of the ellipse 25(x+1)^2+9(y+2)^2=225.

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  19. Find the equation of an ellipse whose axes are the x-and y-axis and...

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  20. If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

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