1
IIT-JEE 2008 Paper 1 Offline
+3
-1
Consider the two curves $${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then,
A
$${C_1}$$ and $${C_2}$$ touch each other only at one point.
B
$${C_1}$$ and $${C_2}$$ touch each other exactly at two points
C
$${C_1}$$ and $${C_2}$$ intersect (but do not touch ) at exactly two points
D
$${C_1}$$ and $${C_2}$$ neither intersect nor touch each other
2
IIT-JEE 2005 Screening
+2
-0.5
The minimum area of triangle formed by the tangent to the $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and coordinate axes is
A
$$ab$$ sq. units
B
$${{{{a^2} + {b^2}} \over 2}}$$ sq. units
C
$${{{{\left( {a + b} \right)}^2}} \over 2}$$ sq. units
D
$${{{a^2} + ab + {b^2}} \over 3}$$ sq. units
3
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
$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$
4
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
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