1
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Out of Syllabus
Consider the parabola with vertex $$\left( {{1 \over 2},{3 \over 4}} \right)$$ and the directrix $$y = {1 \over 2}$$. Let P be the point where the parabola meets the line $$x = - {1 \over 2}$$. If the normal to the parabola at P intersects the parabola again at the point Q, then (PQ)2 is equal to :
A
$${{75} \over 8}$$
B
$${{125} \over {16}}$$
C
$${{25} \over 2}$$
D
$${{15} \over 2}$$
2
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :
A
4(S + R)
B
2(S $$-$$ R)
C
4(S $$-$$ R)
D
2(S + R)
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
If two tangents drawn from a point P to the
parabola y2 = 16(x $$-$$ 3) are at right angles, then the locus of point P is :
A
x + 3 = 0
B
x + 1 = 0
C
x + 2 = 0
D
x + 4 = 0
4
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
Out of Syllabus
A tangent and a normal are drawn at the point P(2, $$-$$4) on the parabola y2 = 8x, which meet the directrix of the parabola at the points A and B respectively. If Q(a, b) is a point such that AQBP is a square, then 2a + b is equal to :
A
$$-$$16
B
$$-$$18
C
$$-$$12
D
$$-$$20
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