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Yukti Vault

Coordinate Geometry

Circle: JEE Main & Advanced PYQs

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

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Questions 251-300 of 305

  1. Two parallel chords of a circle of radius $2$ are at a distance $\sqrt3+1$ apart. If the chords subtend at the center, angles of $\frac{\pi}{k}$ and $\frac{2\pi}{k}$ …
  2. The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4x-5y=20$ to the circle $x^2+y^2=9$ is
  3. Circle(s) touching $x$-axis at a distance 3 from the origin and having an intercept of length $2\sqrt7$ on $y$-axis is (are)
  4. The circle $C_1:x^2+y^2=3$, with centre at $O$, intersects the parabola $x^2=2y$ at the point $P$ in the first quadrant. Let the tangent to the circle $C_1$ at $P$ …
  5. Let $RS$ be the diameter of the circle $x^2+y^2=1$, where $S$ is the point $(1,0)$. Let $P$ be a variable point (other than $R$ and $S$) on the circle and tangents to …
  6. For how many values of $p$, the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points?
  7. Let $O$ be the centre of the circle $x^2+y^2=r^2$, where $r>\frac{\sqrt5}{2}$. Suppose $PQ$ is a chord of this circle and the equation of the line passing through $P$ …
  8. Consider a triangle $\Delta$ whose two sides lie on the x-axis and the line $x+y+1=0$. If the orthocenter of $\Delta$ is $(1,1)$, then the equation of the circle passing …
  9. Let ${}^nC_{r-1}=28$, ${}^nC_r=56$ and ${}^nC_{r+1}=70$. Let $A(4\cos t, 4\sin t)$, $B(2\sin t, -2\cos t)$ and $C(3r-n, r^2-n-1)$ be the vertices of a triangle $ABC$ …
  10. The focus of the parabola $y^2=4x+16$ is the centre of the circle $C$ of radius $5$. If the values of $\lambda$, for which $C$ passes through the point of intersection …
  11. Let the shortest distance from $(a,0)$, $a>0$, to the parabola $y^2=4x$ be $4$. Then the equation of the circle passing through the point $(a,0)$ and the focus of the …
  12. Which of the following is the only CORRECT combination?
  13. Which of the following is the only INCORRECT combination?
  14. The radius of the circle $C$ is ___ .
  15. Consider $M$ with $r=\frac{1025}{513}$. Let $k$ be the number of all those circles $C_n$ that are inside $M$. Let $l$ be the maximum possible number of circles among …
  16. Consider $M$ with $r=\frac{(2^{199}-1)\sqrt{2}}{2^{198}}$. The number of all those circles $D_n$ that are inside $M$ is
  17. The value of $\alpha$ is ___ .
  18. Let $E_1E_2$ and $F_1F_2$ be the chords of $S$ passing through the point $P_0(1,1)$ and parallel to the $x$-axis and the $y$-axis, respectively. Let $G_1G_2$ be the …
  19. The equation of circle $C$ is
  20. A possible equation of $L$ is
  21. A common tangent of the two circles is
  22. Points $E$ and $F$ are given by
  23. Let $P$ be a point on the circle $S$ with both coordinates being positive. Let the tangent to $S$ at $P$ intersect the coordinate axes at the points $M$ and $N$. Then …
  24. Equation of the circle with AB as its diameter is
  25. If $\left(m_i,\dfrac{1}{m_i}\right)$, $m_i>0$, $i=1,2,3,4$ are four distinct points on a circle, then show that $m_1m_2m_3m_4=1$.
  26. A circle passes through three points $A$, $B$ and $C$ with the line segment $AC$ as its diameter. A line passing through $A$ intersects the chord $BC$ at a point $D$ …
  27. The length of the diameter of the circle which touches the $x$-axis at the point $(1,0)$ and passes through the point $(2,3)$ is :
  28. Match the conics in Column I with the statements/expressions in Column II. $$\begin{array}{ll}\textbf{Column I}&\textbf{Column II}\\ (A)\ \text{Circle}&(p)\ \text{The …
  29. Let $C$ be any circle with centre $\left(0,\sqrt2\right)$. Prove that at the most two rational points can lie on $C$. (A rational point is a point both of whose …
  30. $C_1$ and $C_2$ are two concentric circles, the radius of $C_2$ being twice that of $C_1$. From a point $P$ on $C_2$, tangents $PA$ and $PB$ are drawn to $C_1$. Prove …
  31. If two distinct chords, drawn from the point $(\alpha,\beta)$ on the circle $x^{2}+y^{2}=\alpha x+\beta y$ (where $\alpha\beta\neq0$) are bisected by the $y$-axis, then
  32. Let $ABCD$ be a square of side of unit length. Let a circle $C_1$ centered at $A$ with unit radius is drawn. Another circle $C_2$ which touches $C_1$ and the lines $AD$ …
  33. A square is inscribed in the circle $x^{2}+y^{2}-10x-6y+30=0$. One side of this square is parallel to $y=x+3$. If $(x_i,y_i)$ are the vertices of the square, then …
  34. Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersects the circle $C$ at the points $P$ and $Q$. Let $MN$ be a chord …
  35. Let a circle $C$ of radius $1$ and closer to the origin be such that the lines passing through the point $(3,2)$ and parallel to the coordinate axes touch it. Then the …
  36. Let the circle $C_1:x^{2}+y^{2}-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius $2$. If the line of the common chord of $C_1$ and $C_2$ intersects …
  37. Let $ABCD$ and $AEFG$ be squares of side $4$ and $2$ units, respectively. The point $E$ is on the line segment $AB$ and the point $F$ is on the diagonal $AC$. Then the …
  38. If the length of the chord of the circle, $x^{2}+y^{2}=r^{2}$ $(r>0)$ along the line, $y-2x=3$ is $r$, then $r^{2}$ is equal to :
  39. Let the parabola $y=x^{2}+px-3$, meet the coordinate axes at the points $P$, $Q$ and $R$. If the circle $C$ with centre at $(-1,-1)$ passes through the points $P$, $Q$ …
  40. A circle $C$ of radius $2$ lies in the second quadrant and touches both the coordinate axes. Let $r$ be the radius of a circle that has centre at the point $(2,5)$ and …
  41. The centres of a set of circles, each of radius $3$, lie on the circle $x^{2}+y^{2}=25$. The locus of any point in the set is :
  42. The centre of the circle passing through $(0,0)$ and $(1,0)$ and touching the circle $x^{2}+y^{2}=9$ is :
  43. If the two circles $(x-1)^{2}+(y-3)^{2}=r^{2}$ and $x^{2}+y^{2}-8x+2y+8=0$ intersect in two distinct points, then :
  44. A variable circle passes through the fixed point $A(p,q)$ and touches the $x$-axis. The locus of the other end of the diameter through $A$ is :
  45. A circle touches the $x$-axis and also touches the circle with centre at $(0,3)$ and radius $2$. The locus of the centre of the circle is :
  46. Consider a family of circles which are passing through the point $(-1,1)$ and are tangent to the $x$-axis. If $(h,k)$ are the coordinates of the centre of the circles …
  47. If $P$ and $Q$ are the points of intersection of the circles $x^{2}+y^{2}+3x+7y+2p-5=0$ and $x^{2}+y^{2}+2x+2y-p^{2}=0$, then there is a circle passing through $P$, $Q$ …
  48. The two circles $x^{2}+y^{2}=ax$ and $x^{2}+y^{2}=c^{2}$ $(c>0)$ touch each other if :
  49. The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point :
  50. The number of common tangents to the circles $x^{2}+y^{2}-4x-6y-12=0$ and $x^{2}+y^{2}+6x+18y+26=0$, is :

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