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1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The normal at the point$$\left( {bt_1^2,2b{t_1}} \right)$$ on a parabola meets the parabola again in the point $$\left( {bt_2^2,2b{t_2}} \right)$$, then
A
$${t_2} = {t_1} + {2 \over {{t_1}}}$$
B
$${t_2} = -{t_1} - {2 \over {{t_1}}}$$
C
$${t_2} = -{t_1} + {2 \over {{t_1}}}$$
D
$${t_2} = {t_1} - {2 \over {{t_1}}}$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The foci of yhe ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$ and the hyperbola $${{{x^2}} \over {144}} - {{{y^2}} \over {81}} = {1 \over {25}}$$ coincide. Then the value of $${b^2}$$ is
A
$$9$$
B
$$1$$
C
$$5$$
D
$$7$$
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Two common tangents to the circle $${x^2} + {y^2} = 2{a^2}$$ and parabola $${y^2} = 8ax$$ are
A
$$x = \pm \left( {y + 2a} \right)$$
B
$$y = \pm \left( {x + 2a} \right)$$
C
$$x = \pm \left( {y + a} \right)$$
D
$$y = \pm \left( {x + a} \right)$$
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