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Prove that the part of the tangent at an...

Prove that the part of the tangent at any point of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` intercepted between the point of contact and the transvers axis is a harmonic mean between the lengths of the perpendiculars drawn from the foci on the normal at the same point.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
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  2. A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. A tangent drawn to hyperbola x^2/a^2-y^2/b^2 = 1 at P(pi/6) froms a t...

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  19. The normal at a variable point P on the ellipse (x^2)/(a^2)+(y^2)/(b^2...

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  20. If the distance between the foci and the distance between the two d...

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