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Show that the midpoints of focal chords of a hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` lie on another similar hyperbola.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the range of parameter a for which a unique circle will pass thro...

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  2. Column I, Column II stick of length 10 units rests against the floo...

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  3. Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^...

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  4. If the normal at the point P(theta) to the ellipse x^2/14+y^2/5=1 inte...

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  5. A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse ...

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  6. Prove that the part of the tangent at any point of the hyperbola (x^2)...

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  7. A variable line y=m x-1 cuts the lines x=2y and y=-2x at points Aa n d...

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  8. Statement 1 : If aa n db are real numbers and c >0, then the locus rep...

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  9. Two tangents to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having m1a n d...

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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. Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter,...

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  12. Let P be any point on a directrix of an ellipse of eccentricity e ,S b...

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  13. If one of varying central conic (hyperbola) is fixed in magnitude and ...

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  14. If a tangent of slope is 2 of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 i...

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  15. A transvers axis cuts the same branch of a hyperbola (x^2)/(a^2)-(y^2)...

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  16. If (sqrt(3))b x+a y=2a b touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1...

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  17. The eccentricity of the conic represented by x^2-y^2-4x+4y+16=0 is 1 (...

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  18. If the ellipse (x^2)/(a^2-7)+(y^2)/(13=5a)=1 is inscribed in a square ...

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  19. The curve for which the length of the normal is equal to the length...

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  20. The locus of the point of intersection of the tangent at the endpoints...

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