1
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x $$-$$ 1, then the co-ordinates of P are :
A
($$-$$2, 8)
B
(2, 8)
C
(1, 5)
D
(3, 13)
2
JEE Main 2021 (Online) 24th February Morning Slot
+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 = $${a \over 2}$$
3
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies :
A
e4 + 2e2 – 1 = 0
B
e4 + e2 – 1 = 0
C
e2 + 2e – 1 = 0
D
e2 + e – 1 = 0
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
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
$$\left( {{{ - 16} \over 5},{{53} \over {10}}} \right)$$
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