JEE MAINS PRACTICE · Mathematics
Parabola
323 practice questions for JEE Mains Practice — 164 easy · 138 medium · 21 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
An equlateral triangle $S A B$ is inscribed in the parabola $y^2=4 a x$ having its focus at $S$. If chord $A B$ lies towards the lefit of $S$, then side length of this triangle is
MCQ
If the line $y-\sqrt{3} x+3=0$ cuts the parabola $y^2=x+2$ at $A$ and $B$, then $P A \cdot P B$ is equal to where [where $P=(\sqrt{3}, 0)]$.
MCQ
$A B$ is a chord of the parabola $y^2=4 a x$ with vertex $A, B C$ is drawn perpendicular to $A B$ meeting the axis at $C$. The projection of $B C$ on the axis of the parabola is
MCQ
Minimum distance between the curves $y^2=4 x$ and $x^2+y^2-12 x+31=0$ is
MCQ
If two tangents drawn from the point $(h, k)$ to the parabola $y^2=64 x$ be such that the slope of one tangent is 8 times of the other, then the value of $\frac{k^2}{2 h}$ is
MCQ
The curve described parametrically by $x=t^2+t+1, y=t^2-t+1$ represents
MCQ
The equation of directrix of the parabola $y^2+4 y+4 x+2=0$ is
MCQ
Two common tangents to the circle $x^2+y^2=2 a^2$ and parabola $y^2=8 a x$ are
MCQ
The coordinates of the point on the parabola $y=x^2+7 x+2$, which is nearest to the straight line $y=3 x-3$, are
MCQ
If the normal to the parabola $y^2=4 a x$ at the point $\left(a t^2, 2 a t\right)$ cuts the parabola again at $\left(a T^2, 2 a T\right)$, then
MCQ
The mid-point of the line joining the common points of the line $2 x-3 y+8=0$ and $y^2=8 x$ is
MCQ
The equation of the parabola whose vertex is $(-1,-2)$, axis is vertical and which passes through the point $(3,6)$, is