1
IIT-JEE 2004 Screening
+2
-0.5
If tangents are drawn to the ellipse $${x^2} + 2{y^2} = 2,$$ then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is
A
$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$
B
$${1 \over {4{x^2}}} + {1 \over {2{y^2}}} = 1$$
C
$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$
D
$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$
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
The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1,$$ is
A
$$27/4$$ sq. units
B
$$9$$ sq. units
C
$$27/2$$ sq. units
D
$$27$$ sq. units
4
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
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