1
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
2
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Out of Syllabus
Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O(0, 0) to the parabola P which meet P at S and R, then the area (in sq. units) of $$\Delta$$SOR is equal to :
A
$$16\sqrt 2$$
B
16
C
32
D
$$8\sqrt 2$$
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Let P be a variable point on the parabola $$y = 4{x^2} + 1$$. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :
A
$${(3x - y)^2} + (x - 3y) + 2 = 0$$
B
$$2{(3x - y)^2} + (x - 3y) + 2 = 0$$
C
$${(3x - y)^2} + 2(x - 3y) + 2 = 0$$
D
$$2{(x - 3y)^2} + (3x - y) + 2 = 0$$
4
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Out of Syllabus
Let the tangent to the parabola S : y2 = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :
A
$${{25} \over 2}$$
B
$${{35} \over 2}$$
C
$${{15} \over 2}$$
D
25
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