1
AIEEE 2005
+4
-1
Let $$P$$ be the point $$(1, 0)$$ and $$Q$$ a point on the parabola $${y^2} = 8x$$. The locus of mid point of $$PQ$$ is :
A
$${y^2} - 4x + 2 = 0$$
B
$${y^2} + 4x + 2 = 0$$
C
$${x^2} + 4y + 2 = 0$$
D
$${x^2} - 4y + 2 = 0$$
2
AIEEE 2004
+4
-1
If $$a \ne 0$$ and the line $$2bx+3cy+4d=0$$ passes through the points of intersection of the parabolas $${y^2} = 4ax$$ and $${x^2} = 4ay$$, then :
A
$${d^2} + {\left( {3b - 2c} \right)^2} = 0$$
B
$${d^2} + {\left( {3b + 2c} \right)^2} = 0$$
C
$${d^2} + {\left( {2b - 3c} \right)^2} = 0$$
D
$${d^2} + {\left( {2b + 3c} \right)^2} = 0$$
3
AIEEE 2003
+4
-1
Out of Syllabus
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
$${t_2} = {t_1} - {2 \over {{t_1}}}$$
4
AIEEE 2002
+4
-1
Out of Syllabus
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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