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

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 ______________.

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

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 ______________.

3
JEE Main 2022 (Online) 24th June Evening Shift
Numerical
+4
-1

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 = ____________.

4
JEE Main 2021 (Online) 31st August Evening Shift
Numerical
+4
-1
Out of Syllabus
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 ___________.