1
JEE Main 2022 (Online) 27th July Morning Shift
Numerical
+4
-1

If the length of the latus rectum of the ellipse $$x^{2}+4 y^{2}+2 x+8 y-\lambda=0$$ is 4 , and $$l$$ is the length of its major axis, then $$\lambda+l$$ is equal to ____________.

2
JEE Main 2022 (Online) 24th June Morning Shift
Numerical
+4
-1
Out of Syllabus

If two tangents drawn from a point ($$\alpha$$, $$\beta$$) lying on the ellipse 25x2 + 4y2 = 1 to the parabola y2 = 4x are such that the slope of one tangent is four times the other, then the value of (10$$\alpha$$ + 5)2 + (16$$\beta$$2 + 50)2 equals ___________.

3
JEE Main 2021 (Online) 27th August Morning Shift
Numerical
+4
-1
Out of Syllabus
If the minimum area of the triangle formed by a tangent to the ellipse $${{{x^2}} \over {{b^2}}} + {{{y^2}} \over {4{a^2}}} = 1$$ and the co-ordinate axis is kab, then k is equal to _______________.
4
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Out of Syllabus
Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, $$-$$4), one focus at (4, $$-$$4) and one vertex at (5, $$-$$4). If mx $$-$$ y = 4, m > 0 is a tangent to the ellipse E, then the value of 5m2 is equal to _____________.