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Yukti Vault

Coordinate Geometry

Parabola: JEE Main & Advanced PYQs

210 previous year questions on Parabola from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

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Questions 201-210 of 210

  1. If the equation of the parabola with vertex $V\left(\dfrac{3}{2},3\right)$ and the directrix $x+2y=0$ is $\alpha x^{2}+\beta y^{2}-\gamma xy-30x-60y+225=0$, then …
  2. Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the parabola $y^{2}=4x$ with respect to the line $x+y+4=0$. If $d$ denotes …
  3. Two common tangents to the circle $x^{2}+y^{2}=2a^{2}$ and the parabola $y^{2}=8ax$ are :
  4. The normal at the point $\left(bt_1^{2},2bt_1\right)$ on a parabola meets the parabola again in the point $\left(bt_2^{2},2bt_2\right)$, then :
  5. The equation of a tangent to the parabola $y^{2}=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given …
  6. The slope of the line touching both the parabolas $y^{2}=4x$ and $x^{2}=-32y$ is
  7. Given : A circle, $2x^{2}+2y^{2}=5$ and a parabola, $y^{2}=4\sqrt5x$. Statement - 1 : An equation of a common tangent to these curves is $y=x+\sqrt5$. Statement - 2 : If …
  8. Equation of a common tangent to the parabola $y^2=4x$ and the hyperbola $xy=2$ is :
  9. Let $P$ be a variable point on the parabola $y=4x^2+1$. Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to …
  10. If the point on the curve $y^2=6x$, nearest to the point $\left(3,\dfrac{3}{2}\right)$ is $(\alpha,\beta)$, then $2(\alpha+\beta)$ is equal to $\_\_\_\_\_\_\_\_$ .

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