1
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
If the parabolas y2 = 4b(x – c) and y2 = 8ax have a common normal, then which on of the following is a valid choice for the ordered triad (a, b, c) ?
A
(1, 1, 3)
B
(1, 1, 0)
C
$$\left( {{1 \over 2},2,0} \right)$$
D
$$\left( {{1 \over 2},2,3} \right)$$
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
The equation of a tangent to the hyperbola 4x2 – 5y2 = 20 parallel to the line x – y = 2 is -
A
x $$-$$ y + 9 = 0
B
x $$-$$ y $$-$$ 3 = 0
C
x $$-$$ y + 1 = 0
D
x $$-$$ y + 7 = 0
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :
A
$${3 \over 2}$$
B
$$\sqrt 3$$
C
2
D
$${2 \over {\sqrt 3 }}$$
4
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Let A(4, $$-$$ 4) and B(9, 6) be points on the parabola, y2 = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of $$\Delta$$ACB is maximum. Then, the area (in sq. units) of $$\Delta$$ACB, is :
A
$$31{1 \over 4}$$
B
$$30{1 \over 2}$$
C
32
D
$$31{3 \over 4}$$
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