1
JEE Main 2021 (Online) 20th July Evening Shift
Numerical
+4
-1
If the point on the curve y2 = 6x, nearest to the point $$\left( {3,{3 \over 2}} \right)$$ is ($$\alpha$$, $$\beta$$), then 2($$\alpha$$ + $$\beta$$) is equal to _____________.
2
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
Out of Syllabus
Let y = mx + c, m > 0 be the focal chord of y2 = $$-$$ 64x, which is tangent to (x + 10)2 + y2 = 4. Then, the value of 4$$\sqrt 2$$ (m + c) is equal to _____________.
3
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
Out of Syllabus
A line is a common tangent to the circle (x $$-$$ 3)2 + y2 = 9 and the parabola y2 = 4x. If the two points of contact (a, b) and (c, d) are distinct and lie in the first quadrant, then 2(a + c) is equal to _________.
4
JEE Main 2020 (Online) 3rd September Evening Slot
Numerical
+4
-0
Out of Syllabus
If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ________ .