1
IIT-JEE 2005 Screening
+2
-0.5
Tangent to the curve $$y = {x^2} + 6$$ at a point $$(1, 7)$$ touches the circle $${x^2} + {y^2} + 16x + 12y + c = 0$$ at a point $$Q$$. Then the coordinates of $$Q$$ are
A
$$(-6, -11)$$
B
$$(-9, -13)$$
C
$$(-10, -15)$$
D
$$(-6, -7)$$
2
IIT-JEE 2004 Screening
+2
-0.5
The angle between the tangents drawn from the point $$(1, 4)$$ to the parabola $${y^2} = 4x$$ is
A
$$\pi /6$$
B
$$\pi /4$$
C
$$\pi /3$$
D
$$\pi /2$$
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 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
$$\left( {4, - \,\sqrt 6 } \right)$$
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