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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 151-200 of 210

  1. Let $ABCD$ be a square of side length $2$ units. $C_2$ is the circle through the vertices $A,B,C,D$ and $C_1$ is the circle touching all the sides of the square $ABCD$. …
  2. The equations of the common tangents to the parabola $y=x^2$ and $y=-(x-2)^2$ is/are
  3. Let $ABCD$ be a square of side length $2$ units. $C_2$ is the circle through the vertices $A,B,C,D$ and $C_1$ is the circle touching all the sides of the square $ABCD$. …
  4. Normals are drawn at points $P,Q$ and $R$ lying on the parabola $y^2=4x$ which intersect at $(3,0)$. Then Column I: (i) Area of $\triangle PQR$; (ii) Radius of …
  5. If the chord joining the points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ on the parabola $y^2=12x$ subtends a right angle at the vertex of the parabola, then $x_1x_2-y_1y_2$ is …
  6. Let chord $PQ$ of length $3\sqrt{13}$ of the parabola $y^{2}=12x$ be such that the ordinates of points $P$ and $Q$ are in the ratio $1:2$. If the chord $PQ$ subtends an …
  7. Let $P$ be a moving point on the circle $x^{2}+y^{2}-6x-8y+21=0$. Then, the maximum distance of $P$ from the vertex of the parabola $x^{2}+6x+y+13=0$ is equal to :
  8. Let $E$ denote the parabola $y^2=8x$. Let $P=(-2,4)$, and let $Q$ and $Q'$ be two distinct points on $E$ such that the lines $PQ$ and $PQ'$ are tangents to $E$. Let $F$ …
  9. Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^2=4x$ be the curve $S$. Let $P$ be any point on $S$. Then the locus of the point …
  10. Let $O$ be the vertex of the parabola $x^2=4y$ and $Q$ be any point on it. Let the locus of the point $P$, which divides the line segment $OQ$ internally in the ratio …
  11. Let one end of a focal chord of the parabola $y^2=16x$ be $(16,16)$. If $P(\alpha,\beta)$ divides this focal chord internally in the ratio $5:2$, then the minimum value …
  12. Let $y^2=12x$ be the parabola with its vertex at $O$. Let $P$ be on the parabola and $A$ be a point on the $x$-axis such that $\angle OPA=90^\circ$. Then the locus of …
  13. An equilateral triangle $OAB$ is inscribed in the parabola $y^2=4x$ with the vertex $O$ at the vertex of the parabola. Then the minimum distance of the circle having …
  14. Let the image of the parabola $x^2=4y$ in the line $x-y=1$ be $(y+a)^2=b(x-c)$, $a,b,c\in\mathbf{N}$. Then $a+b+c$ is equal to :
  15. Let $A$ be the focus of the parabola $y^2=8x$. Let the line $y=mx+c$ intersect the parabola at two distinct points $B$ and $C$. If the centroid of the triangle $ABC$ is …
  16. STATEMENT-1: The curve $y=\frac{-x^2}{2}+x+1$ is symmetric with respect to the line $x=1$. because STATEMENT-2: A parabola is symmetric about its axis.
  17. Consider the two curves $C_1: y^2=4x$, $C_2: x^2+y^2-6x+1=0$. Then,
  18. Consider the parabola $y^2=8x$. Let $\Delta_1$ be the area of the triangle formed by the end points of its latus rectum and the point $P\left(\frac12,2\right)$ on the …
  19. A line $L: y=mx+3$ meets $y$-axis at $E(0,3)$ and the arc of the parabola $y^2=16x$, $0\leq y\leq6$ at the point $F(x_0,y_0)$. The tangent to the parabola at …
  20. The common tangents to the circle $x^2+y^2=2$ and the parabola $y^2=8x$ touch the circle at the points $P,Q$ and the parabola at the points $R,S$. Then the area of the …
  21. The tangent $PT$ and the normal $PN$ to the parabola $y^2=4ax$ at a point $P$ on it meet its axis at points $T$ and $N$, respectively. The locus of the centroid of the …
  22. Let $(x,y)$ be any point on the parabola $y^2=4x$. Let $P$ be the point that divides the line segment from $(0,0)$ to $(x,y)$ in the ratio $1:3$. Then the locus of $P$ is
  23. Let $L$ be a normal to the parabola $y^2=4x$. If $L$ passes through the point $(9,6)$, then $L$ is given by
  24. Let $S$ be the focus of the parabola $y^2=8x$ and let $PQ$ be the common chord of the circle $x^2+y^2-2x-4y=0$ and the given parabola. The area of the triangle $PQS$ is
  25. Let the curve $C$ be the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $A$ and $B$ are the points of intersection of $C$ with the line …
  26. If the normals of the parabola $y^2=4x$ drawn at the end points of its latus rectum are tangents to the circle $(x-3)^2+(y+2)^2=r^2$, then the value of $r^2$ is
  27. Let $P$ and $Q$ be distinct points on the parabola $y^2=2x$ such that a circle with $PQ$ as diameter passes through the vertex $O$ of the parabola. If $P$ lies in the …
  28. Suppose that the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ are $(f_1,0)$ and $(f_2,0)$ where $f_1>0$ and $f_2<0$. Let $P_1$ and $P_2$ be two parabolas with a …
  29. If a chord, which is not a tangent, of the parabola $y^2=16x$ has the equation $2x+y=p$, and midpoint $(h,k)$, then which of the following is(are) possible value(s) of …
  30. Let $ABCD$ be a trapezium whose vertices lie on the parabola $y^2=4x$. Let the sides $AD$ and $BC$ of the trapezium be parallel to $y$-axis. If the diagonal $AC$ is of …
  31. The ratio of the areas of the triangles $PQS$ and $PQR$ is
  32. Length of chord $PQ$ is
  33. The value of $r$ is
  34. If $st=1$, then the tangent at $P$ and the normal at $S$ to the parabola meet at a point whose ordinate is
  35. If a tangent to a suitable conic (Column 1) is found to be $y=x+8$ and its point of contact is $(8,16)$, then which of the following options is the only CORRECT …
  36. The radius of the circumcircle of the triangle $PRS$ is
  37. If chord $PQ$ subtends an angle $\theta$ at the vertex of $y^2=4ax$, then $\tan\theta=$
  38. The equation of the locus of the point whose distances from the point $P$ and the line $AB$ are equal, is
  39. The radius of the incircle of the triangle $PQR$ is
  40. Suppose that the normals drawn at three different points on the parabola $y^{2}=4x$ pass through the point $(h,k)$. Show that $h>2$.
  41. The angle between a pair of tangents drawn from a point $P$ to the parabola $y^{2}=4ax$ is $45^\circ$. Show that the locus of the point $P$ is a hyperbola.
  42. This question has Statement 1 and Statement 2. Of the four options given after the Statements, choose the one that best describes the two Statements. Statement 1 : An …
  43. If the three normals drawn to the parabola, $y^{2}=2x$ pass through the point $(a,0)$, $a\neq0$, then '$a$' must be greater than :
  44. Let the length of the focal chord $PQ$ of the parabola $y^{2}=12x$ be $15$ units. If the distance of $PQ$ from the origin is $p$, then $10p^{2}$ is equal to …
  45. Let $PQ$ be a chord of the parabola $y^{2}=12x$ and the midpoint of $PQ$ be at $(4,1)$. Then, which of the following point lies on the line passing through the points …
  46. Suppose $AB$ is a focal chord of the parabola $y^{2}=12x$ of length $l$ and slope $m<\sqrt{3}$. If the distance of the chord $AB$ from the origin is $d$, then $ld^{2}$ …
  47. Let a line perpendicular to the line $2x-y=10$ touch the parabola $y^{2}=4(x-9)$ at the point $P$. The distance of the point $P$ from the centre of the circle …
  48. Let $L_1$ be a tangent to the parabola $y^{2}=4(x+1)$ and $L_2$ be a tangent to the parabola $y^{2}=8(x+2)$ such that $L_1$ and $L_2$ intersect at right angles. Then …
  49. Let $P\left(4,4\sqrt{3}\right)$ be a point on the parabola $y^{2}=4ax$ and $PQ$ be a focal chord of the parabola. If $M$ and $N$ are the foot of perpendiculars drawn …
  50. If the line $3x-2y+12=0$ intersects the parabola $4y=3x^{2}$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment $AB$ subtends an angle equal …

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