1
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1
Out of Syllabus

Let P : y2 = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of $${\pi \over 4}$$ with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is :

A
8 only
B
2 only
C
$${1 \over 4}$$ only
D
any a > 0
2
JEE Main 2022 (Online) 29th June Morning Shift
+4
-1

Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of $${\pi \over 2}$$ at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, $${a^2} > {b^2}$$. If e is the eccentricity of the ellipse E, then the value of $${1 \over {{e^2}}}$$ is equal to :

A
$$1 + \sqrt 2$$
B
$$3 + 2\sqrt 2$$
C
$$1 + 2\sqrt 3$$
D
$$4 + 5\sqrt 3$$
3
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

If vertex of a parabola is (2, $$-$$1) and the equation of its directrix is 4x $$-$$ 3y = 21, then the length of its latus rectum is :

A
2
B
8
C
12
D
16
4
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $$3x + y - 29 = 0$$, is $${x^2} + a{y^2} + bxy + cx + dy + k = 0$$, then $$a + b + c + d + k$$ is equal to :

A
575
B
$$-$$575
C
576
D
$$-$$576
EXAM MAP
Medical
NEET