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Let x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^...

Let `x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1` be confocal `(a > A and a> b)` having the foci at `s_1 and S_2,` respectively. If P is their point of intersection, then `S_1 P and S_2 P` are the roots of quadratic equation

A

(a) `x^(2)+2Ax+(a^(2)-A^(2))=0`

B

(b) `x^(2)+2ax+(a^(2)-A^(2))=0`

C

(c) `x^(2)-2Ax+(a^(2)+A^(2))=0`

D

(d) `x^(2)-2ax+(a^(2)-A^(2))=0`

Text Solution

Verified by Experts

The correct Answer is:
D
`S_(1)+S_(2)P=2a and S_(1)P-S_(2)P=2A`
`S_(1)+=a+A and S_(2)P=(a-A)`
Required quadratic equation is `x^(2)-2ax+(a^(2)-A^(2))=0`
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CENGAGE PUBLICATION-HYPERBOLA-EXERCISES
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  2. If the distances of one focus of hyperbola from its directrices are 5 ...

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  3. Let x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1 be confocal (a > A and a> ...

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  4. Two tangents are drawn from a point on hyperbola x^(2)-y^(2)=5 to the...

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  5. Equation of the rectangular hyperbola whose focus is (1,-1) and the co...

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  6. If two circles (x+4)^(2)+y^(2)=1 and (x-4)^(2)+y^(2)=9 are touched ext...

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  7. If the vertex of a hyperbola bisects the distance between its center ...

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  8. The eccentricity of the hyperbola whose length of the latus rectum is ...

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  9. Let L L ' be the latus rectum through the focus of the hyperbola (x^2)...

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  10. The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=...

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  11. The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 ...

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  12. lf the eccentricity of the hyperbola x^2 - y^2 sec^2 alpha=5 is sqrt3...

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  13. The equation of the transvers and conjugate axes of a hyperbola are, ...

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  14. Factorise the expression: (x^2–2xy+y^2)–z^2

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  15. If two points P & Q on the hyperbola ,x^2/a^2-y^2/b^2=1 whose centre i...

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  16. The angle between the lines joining the origin to the points of inters...

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  17. A variable chord of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(b > a), s...

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  18. If the distance between two parallel tangents having slope m drawn to ...

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  19. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

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  20. 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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