1
JEE Main 2023 (Online) 10th April Morning Shift
Numerical
+4
-1

Let a common tangent to the curves $${y^2} = 4x$$ and $${(x - 4)^2} + {y^2} = 16$$ touch the curves at the points P and Q. Then $${(PQ)^2}$$ is equal to _________.

2
JEE Main 2023 (Online) 8th April Evening Shift
Numerical
+4
-1

The ordinates of the points P and $$\mathrm{Q}$$ on the parabola with focus $$(3,0)$$ and directrix $$x=-3$$ are in the ratio $$3: 1$$. If $$\mathrm{R}(\alpha, \beta)$$ is the point of intersection of the tangents to the parabola at $$\mathrm{P}$$ and $$\mathrm{Q}$$, then $$\frac{\beta^{2}}{\alpha}$$ is equal to _______________.

3
JEE Main 2023 (Online) 6th April Morning Shift
Numerical
+4
-1

Let the tangent to the curve $$x^{2}+2 x-4 y+9=0$$ at the point $$\mathrm{P}(1,3)$$ on it meet the $$y$$-axis at $$\mathrm{A}$$. Let the line passing through $$\mathrm{P}$$ and parallel to the line $$x-3 y=6$$ meet the parabola $$y^{2}=4 x$$ at $$\mathrm{B}$$. If $$\mathrm{B}$$ lies on the line $$2 x-3 y=8$$, then $$(\mathrm{AB})^{2}$$ is equal to ___________.

4
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

If the $$x$$-intercept of a focal chord of the parabola $$y^{2}=8x+4y+4$$ is 3, then the length of this chord is equal to ____________.

JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination