1
JEE Main 2022 (Online) 27th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

A circle of radius 2 unit passes through the vertex and the focus of the parabola y2 = 2x and touches the parabola $$y = {\left( {x - {1 \over 4}} \right)^2} + \alpha $$, where $$\alpha$$ > 0. Then (4$$\alpha$$ $$-$$ 8)2 is equal to ______________.

Your input ____
2
JEE Main 2022 (Online) 26th June Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let the common tangents to the curves $$4({x^2} + {y^2}) = 9$$ and $${y^2} = 4x$$ intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and l respectively denote the eccentricity and the length of the latus rectum of this ellipse, then $${l \over {{e^2}}}$$ is equal to ______________.

Your input ____
3
JEE Main 2022 (Online) 24th June Evening Shift
Numerical
+4
-1
Change Language

Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6. Then the directrix of P2 is x + 2y = ____________.

Your input ____
4
JEE Main 2021 (Online) 31st August Evening Shift
Numerical
+4
-1
Out of Syllabus
Change Language
A tangent line L is drawn at the point (2, $$-$$4) on the parabola y2 = 8x. If the line L is also tangent to the circle x2 + y2 = a, then 'a' is equal to ___________.
Your input ____
JEE Main Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12