1
IIT-JEE 2007
+3
-0.75
A hyperbola, having the transverse axis of length $$2\sin \theta ,$$ is confocal with the ellipse $$3{x^2} + 4{y^2} = 12.$$ Then its equation is
A
$${x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1$$
B
$${x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1$$
C
$${x^2}{\sin ^2}\theta - {y^2}co{s^2}\theta = 1$$
D
$${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1$$
2
IIT-JEE 2004 Screening
+2
-0.5
If the line $$62x + \sqrt 6 y = 2$$ touches the hyperbola $${x^2} - 2{y^2} = 4$$, then the point of contact is
A
$$\left( { - 2,\,\sqrt 6 } \right)$$
B
$$\left( { - 5,\,2\sqrt 6 } \right)$$
C
$$\left( {{1 \over 2},{1 \over {\sqrt 6 }}} \right)$$
D
$$\left( {4, - \,\sqrt 6 } \right)$$
3
IIT-JEE 2003 Screening
+2
-0.5
For hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$ which of the following remains constant with change in $$'\alpha '$$
A
abscissae of vertices
B
abscissae of foci
C
eccentricity
D
directrix
4
IIT-JEE 1999
+2
-0.5
Let $$P$$ $$\left( {a\,\sec \,\theta ,\,\,b\,\tan \theta } \right)$$ and $$Q$$ $$\left( {a\,\sec \,\,\phi ,\,\,b\,\tan \,\phi } \right)$$, where $$\theta + \phi = \pi /2,$$, be two points on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$.

If $$(h, k)$$ is the point of intersection of the normals at $$P$$ and $$Q$$, then $$k$$ is equal to

A
$${{{a^2} + {b^2}} \over a}$$
B
$$- \left( {{{{a^2} + {b^2}} \over a}} \right)$$
C
$${{{a^2} + {b^2}} \over b}$$
D
$$- \left( {{{{a^2} + {b^2}} \over b}} \right)$$
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