1
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
The locus of the mid-point of the line segment joining the focus of the parabola y2 = 4ax to a moving point of the parabola, is another parabola whose directrix is :
A
x = 0
B
x = - $${a \over 2}$$
C
x = a
D
x = $${a \over 2}$$
2
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Out of Syllabus
The centre of the circle passing through the point (0, 1) and touching the parabola
y = x2 at the point (2, 4) is :
A
$$\left( {{6 \over 5},{{53} \over {10}}} \right)$$
B
$$\left( {{3 \over {10}},{{16} \over 5}} \right)$$
C
$$\left( {{{ - 53} \over {10}},{{16} \over 5}} \right)$$
D
$$\left( {{{ - 16} \over 5},{{53} \over {10}}} \right)$$
3
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
Out of Syllabus
Let L1 be a tangent to the parabola y2 = 4(x + 1)
and L2 be a tangent to the parabola y2 = 8(x + 2)
such that L1 and L2 intersect at right angles. Then L1 and L2 meet on the straight line :
A
x + 3 = 0
B
x + 2y = 0
C
x + 2 = 0
D
2x + 1 = 0
4
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
Out of Syllabus
If the common tangent to the parabolas,
y2 = 4x and x2 = 4y also touches the circle, x2 + y2 = c2,
then c is equal to :
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over {2\sqrt 2 }}$$
C
$${1 \over 2}$$
D
$${1 \over 4}$$
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