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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 1-50 of 305

  1. Let $A(1,4)$ and $B(1,-5)$ be two points. Let $P$ be a point on the circle $(x-1)^{2}+(y-1)^{2}=1$ such that $(PA)^{2}+(PB)^{2}$ have maximum value, then the points …
  2. Choose the correct statement about two circles whose equations are given below : $x^{2}+y^{2}-10x-10y+41=0$ $x^{2}+y^{2}-22x-10y+137=0$
  3. Let the tangent to the circle $x^{2}+y^{2}=25$ at the point $R(3,4)$ meet $x$-axis and $y$-axis at points $P$ and $Q$, respectively. If $r$ is the radius of the circle …
  4. The sum of the values of '$a$' for which circles of radius $\frac{\sqrt{5}}{3}$, touch the straight lines, $x-2y-a=0$ and $3x-6y+7=0$, is
  5. Consider a family of circles which pass through the point $(1,1)$ and touch the axis of $y$. If the centre of such a circle is at $(h,k)$, then the set of all values of …
  6. Let the lengths of intercepts on $x$-axis and $y$-axis made by the circle $x^{2}+y^{2}+ax+2ay+c=0$, $(a<0)$ be $2\sqrt{2}$ and $2\sqrt{5}$, respectively. Then the …
  7. Let the circle $S:36x^{2}+36y^{2}-108x+120y+C=0$ be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, $x-2y=4$ …
  8. Choose the incorrect statement about the two circles whose equations are given below : $x^{2}+y^{2}-10x-10y+41=0$ and $x^{2}+y^{2}-16x-10y+80=0$
  9. Two tangents are drawn from a point $P$ to the circle $x^{2}+y^{2}-2x-4y+4=0$, such that the angle between these tangents is $\tan^{-1}\left(\frac{12}{5}\right)$, where …
  10. For the four circles $M,N,O$ and $P$, following four equations are given : Circle $M:x^{2}+y^{2}=1$ Circle $N:x^{2}+y^{2}-2x=0$ Circle $O:x^{2}+y^{2}-2x-2y+1=0$ Circle …
  11. If the locus of the mid-point of the line segment from the point $(3,2)$ to a point on the circle, $x^{2}+y^{2}=1$ is a circle of radius $r$, then $r$ is equal to :
  12. Let the point $P$ be the vertex of the parabola $y=x^{2}-6x+12$. If a line passing through the point $P$ intersects the circle $x^{2}+y^{2}-2x-4y+3=0$ at the points $R$ …
  13. Let $C$ be a circle having centre in the first quadrant and touching the $x$-axis at a distance of $3$ units from the origin. If the circle $C$ has an intercept of …
  14. The line $2x-y+1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2y=4$. Then, the radius of the circle is :
  15. Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $x+(k-1)y+3=0$ and $2x+k^{2}y-4=0$. If the line …
  16. A circle $C$ touches the line $x=2y$ at the point $(2,1)$ and intersects the circle $C_1:x^{2}+y^{2}+2y-5=0$ at two points $P$ and $Q$ such that $PQ$ is a diameter of …
  17. A circle touches the $y$-axis at the point $(0,4)$ and passes through the point $(2,0)$. Which of the following lines is not a tangent to this circle ?
  18. If the circles $(x+1)^{2}+(y+2)^{2}=r^{2}$ and $x^{2}+y^{2}-4x-4y+4=0$ intersect at exactly two distinct points, then
  19. If a line, $y=mx+c$ is a tangent to the circle, $(x-3)^2+y^2=1$ and it is perpendicular to a line $L_1$, where $L_1$ is the tangent to the circle, $x^2+y^2=1$ at the …
  20. If one of the diameters of the circle $x^{2}+y^{2}-2x-6y+6=0$ is a chord of another circle '$C$', whose center is at $(2,1)$, then its radius is $\_\_\_\_\_\_$ .
  21. The number of common tangents, to the circles $x^{2}+y^{2}-18x-15y+131=0$ and $x^{2}+y^{2}-6x-6y-7=0$, is
  22. If the common tangent to the parabolas, $y^2=4x$ and $x^2=4y$ also touches the circle, $x^2+y^2=c^2$, then $c$ is equal to :
  23. A circle is inscribed in an equilateral triangle of side length $12$. If the area and perimeter of any square inscribed in this circle are $m$ and $n$, respectively …
  24. If the locus of the point, whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5:4$, is $ax^{2}+by^{2}+cxy+dx+ey+170=0$, then the value of …
  25. Let $A=\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid2x^2+2y^2-2x-2y=1\}$, $B=\{(x,y)\in\mathbf{R}\times\mathbf{R}\mid4x^2+4y^2-16y+7=0\}$ and …
  26. Let the tangents at two points $A$ and $B$ on the circle $x^2+y^2-4x+3=0$ meet at origin $O(0,0)$. Then the area of the triangle $OAB$ is :
  27. Let $P$ and $Q$ be two distinct points on a circle which has center at $C(2,3)$ and which passes through origin $O$. If $OC$ is perpendicular to both the line segments …
  28. Let the centre of a circle $C$ be $(\alpha,\beta)$ and its radius $r<8$. Let $3x+4y=24$ and $3x-4y=32$ be two tangents and $4x+3y=1$ be a normal to $C$. Then …
  29. Let $C$ be the centre of the circle $x^2+y^2-x+2y=\frac{11}{4}$ and $P$ be a point on the circle. A line passes through the point $C$, makes an angle of $\frac\pi4$ with …
  30. Let the line $x-y=4$ intersect the circle $C:(x-4)^{2}+(y+3)^{2}=9$ at the points $Q$ and $R$. If $P(\alpha,\beta)$ is a point on $C$ such that $PQ=PR$, then …
  31. If the tangents at the points $P$ and $Q$ on the circle $x^{2}+y^{2}-2x+y=5$ meet at the point $R\left(\frac{9}{4},2\right)$, then the area of the triangle $PQR$ is:
  32. A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$. Let $f(x,y)=0$ be the locus of $P$, which intersects the …
  33. Consider a circle $C$ which touches the $y$-axis at $(0,6)$ and cuts off an intercept $6\sqrt5$ on the $x$-axis. Then the radius of the circle $C$ is equal to :
  34. If $x^{2}+9y^{2}-4x+3=0$, $x,y\in\mathbf{R}$, then $x$ and $y$ respectively lie in the intervals :
  35. The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^2$ at the point $(2,4)$ is :
  36. Let the tangent to the circle $C_1:x^{2}+y^{2}=2$ at the point $M(-1,1)$ intersect the circle $C_2:(x-3)^{2}+(y-2)^{2}=5$, at two distinct points $A$ and $B$. If the …
  37. Let the abscissae of the two points $P$ and $Q$ on a circle be the roots of $x^2-4x-6=0$ and the ordinates of $P$ and $Q$ be the roots of $y^2+2y-7=0$. If $PQ$ is a …
  38. If a line along a chord of the circle $4x^{2}+4y^{2}+120x+675=0$, passes through the point $(-30,0)$ and is tangent to the parabola $y^{2}=30x$, then the length of this …
  39. Two tangents are drawn from the point $P(-1,1)$ to the circle $x^2+y^2-2x-6y+6=0$. If these tangents touch the circle at points $A$ and $B$, and if $D$ is a point on the …
  40. A line segment $AB$ of length $\lambda$ moves such that the points $A$ and $B$ remain on the periphery of a circle of radius $\lambda$. Then the locus of the point, that …
  41. Let $\left(5,\frac{a}{4}\right)$ be the circumcenter of a triangle with vertices $A(a,-2)$, $B(a,6)$ and $C\left(\frac{a}{4},-2\right)$. Let $\alpha$ denote the …
  42. If the four distinct points $(4,6)$, $(-1,5)$, $(0,0)$ and $(k,3k)$ lie on a circle of radius $r$, then $10k+r^{2}$ is equal to
  43. A circle $C_1$ passes through the origin $O$ and has diameter $4$ on the positive $x$-axis. The line $y=2x$ gives a chord $OA$ of circle $C_1$. Let $C_2$ be the circle …
  44. The set of values of $k$, for which the circle $C:4x^{2}+4y^{2}-12x+8y+k=0$ lies inside the fourth quadrant and the point $\left(1,-\frac{1}{3}\right)$ lies on or inside …
  45. Let $O$ be the origin and $OP$ and $OQ$ be the tangents to the circle $x^{2}+y^{2}-6x+4y+8=0$ at the points $P$ and $Q$ on it. If the circumcircle of the triangle $OPQ$ …
  46. Four distinct points $(2k,3k)$, $(1,0)$, $(0,1)$ and $(0,0)$ lie on a circle for $k$ equal to :
  47. Let $A$ be the point $(1,2)$ and $B$ be any point on the curve $x^{2}+y^{2}=16$. If the centre of the locus of the point $P$, which divides the line segment $AB$ in the …
  48. Consider three circles : $C_1:x^{2}+y^{2}=r^{2}$ $C_2:(x-1)^{2}+(y-1)^{2}=r^{2}$ $C_3:(x-2)^{2}+(y-1)^{2}=r^{2}$ If a line $L:y=mx+c$ be a common tangent to $C_1$, $C_2$ …
  49. Consider the circle $C:x^{2}+y^{2}-6x-8y-11=0$. Let a variable chord $AB$ of the circle $C$ subtend a right angle at the origin. If the locus of the foot of the …
  50. Let $C:x^{2}+y^{2}=4$ and $C':x^{2}+y^{2}-4\lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles $C$ and $C'$ intersect at two …

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