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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 201-250 of 305

  1. The locus of the mid-point of a chord of the circle $x^{2}+y^{2}=4$ which subtends a right angle at the origin is
  2. Two circles, each of radius $5$ units, touch each other at $(1,2)$. If the equation of their common tangent is $4x+3y=10$, find the equation of the circles.
  3. State TRUE or FALSE: The line $x+3y=0$ is a diameter of the circle $x^{2}+y^{2}-6x+2y=0$.
  4. Let a circle be given by $2x(x-a)+y(2y-b)=0$, $(a\neq0,\ b\neq0)$. Find the condition on $a$ and $b$ if two chords, each bisected by the $x$-axis, can be drawn to the …
  5. From the point $A(0,3)$ on the circle $x^{2}+4x+(y-3)^{2}=0$, a chord $AB$ is drawn and extended to a point $M$ such that $AM=2AB$. The equation of the locus of $M$ is …
  6. Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is $4$. Find the ratio of the …
  7. The lines $2x-3y=5$ and $3x-4y=7$ are diameters of a circle of area $154$ sq. units. Then the equation of this circle is
  8. The lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to the same circle. The radius of this circle is ______.
  9. From the origin chords are drawn to the circle $(x-1)^{2}+y^{2}=1$. The equation of the locus of the mid-points of these chords is ______.
  10. If the circle $x^{2}+y^{2}=a^{2}$ intersects the hyperbola $xy=c^{2}$ in four points $P(x_1,y_1)$, $Q(x_2,y_2)$, $R(x_3,y_3)$, $S(x_4,y_4)$, then
  11. If the circles $x^{2}+y^{2}+2x+2ky+6=0$, $x^{2}+y^{2}+2ky+k=0$ intersect orthogonally, then $k$ is
  12. Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the …
  13. Let $AB$ be a chord of the circle $x^{2}+y^{2}=r^{2}$ subtending a right angle at the centre. Then the locus of the centroid of the triangle $PAB$ as $P$ moves on the …
  14. The number of common tangents to the circles $x^{2}+y^{2}=4$ and $x^{2}+y^{2}-6x-8y=24$ is
  15. Let $T_1,T_2$ be two tangents drawn from $(-2,0)$ onto the circle $C:x^{2}+y^{2}=1$. Determine the circles touching $C$ and having $T_1,T_2$ as their pair of tangents. …
  16. The triangle $PQR$ is inscribed in the circle $x^{2}+y^{2}=25$. If $Q$ and $R$ have co-ordinates $(3,4)$ and $(-4,3)$ respectively, then $\angle QPR$ is equal to
  17. Let $C_1$ and $C_2$ be two circles with $C_2$ lying inside $C_1$. A circle $C$ lying inside $C_1$ touches $C_1$ internally and $C_2$ externally. Identify the locus of …
  18. The circles $x^{2}+y^{2}-10x+16=0$ and $x^{2}+y^{2}=r^{2}$ intersect each other in two distinct points if
  19. The angle between a pair of tangents drawn from a point $P$ to the circle $x^{2}+y^{2}+4x-6y+9\sin^{2}\alpha+13\cos^{2}\alpha=0$ is $2\alpha$. The equation of the locus …
  20. Find the intervals of values of $a$ for which the line $y+x=0$ bisects two chords drawn from a point $\left(\dfrac{1+\sqrt2a}{2},\dfrac{1-\sqrt2a}{2}\right)$ to the …
  21. The chords of contact of the pair of tangents drawn from each point on the line $2x+y=4$ to the circle $x^{2}+y^{2}=1$ pass through the point ______.
  22. Let $2x^{2}+y^{2}-3xy=0$ be the equation of a pair of tangents drawn from the origin $O$ to a circle of radius $3$ with centre in the first quadrant. If $A$ is one of …
  23. Let $L_1$ be a straight line passing through the origin and $L_2$ be the straight line $x+y=1$. If the intercepts made by the circle $x^{2}+y^{2}-x+3y=0$ on $L_1$ and …
  24. The intercept on the line $y=x$ by the circle $x^{2}+y^{2}-2x=0$ is $AB$. Equation of the circle with $AB$ as a diameter is ______.
  25. If two distinct chords, drawn from the point $(p,q)$ on the circle $x^{2}+y^{2}=px+qy\ (\text{where }pq\neq0)$ are bisected by the $x$-axis, then
  26. If $a>2b>0$ then the positive value of $m$ for which $y=mx-b\sqrt{1+m^{2}}$ is a common tangent to $x^{2}+y^{2}=b^{2}$ and $(x-a)^{2}+y^{2}=b^{2}$ is
  27. Find the equation of the circle touching the line $2x+3y+1=0$ at $(1,-1)$ and cutting orthogonally the circle having the line segment joining $(0,3)$ and $(-2,-1)$ as …
  28. The tangent to the curve $y=x^{2}+6$ at the point $(1,7)$ touches the circle $x^{2}+y^{2}+16x+12y+c=0$ at a point $Q$. Then the coordinates of $Q$ are
  29. Circles with radii $3$, $4$ and $5$ touch each other externally. If $P$ is the point of intersection of the tangents to these circles at their points of contact, find …
  30. 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 $ABCD$. …
  31. The area of the equilateral triangle, in which three coins, each of radius $1$ cm, are placed as shown in the figure, is
  32. If the tangent at the point $P$ on the circle $x^{2}+y^{2}+6x+6y=2$ meets a straight line $5x-2y+6=0$ at a point $Q$ on the $y$-axis, then the length of $PQ$ is
  33. The centre of circle inscribed in square formed by the lines $x^2-8x+12=0$ and $y^2-14y+45=0$, is
  34. A circle is given by $x^{2}+(y-1)^{2}=1$, another circle $C$ touches it externally and also the $x$-axis, then the locus of its centre is
  35. If one of the diameters of the circle $x^{2}+y^{2}-2x-6y+6=0$ is a chord to the circle with centre $(2,1)$, then the radius of the circle is
  36. For the circle $x^2+y^2=r^2$, find the value of $r$ for which the area enclosed by the tangents drawn from the point $P(6,8)$ to the circle and the chord of contact is …
  37. If $P$ is a point on the circle $x^2+y^2=4$, $Q$ is a point on the straight line $5x+y+2=0$ and $x-y+1=0$ is the perpendicular bisector of $PQ$, then $13$ times the sum …
  38. Let $y=x$ be the equation of a chord of the circle $C_1$ (in the closed half-plane $x\ge0$) of diameter $10$ passing through the origin. Let $C_2$ be another circle …
  39. Let a circle $C$ have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If …
  40. Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^{2}+y^{2}+x-3y=0$ are bisected by the $y$-axis. If the other ends of these chords are $R$ and $S$ …
  41. Let the set of all values of $r$, for which the circles $(x+1)^2+(y+4)^2=r^2$ and $x^2+y^2-4x-2y-4=0$ intersect at two distinct points, be the interval $(\alpha,\beta)$. …
  42. Let $PQ$ and $MN$ be two straight lines touching the circle $x^2+y^2-4x-6y-3=0$ at the points $A$ and $B$ respectively. Let $O$ be the centre of the circle and …
  43. Let a circle of radius $4$ pass through the origin $O$, the points $A(-\sqrt3a,0)$ and $B(0,-\sqrt2b)$, where $a$ and $b$ are real parameters and $ab\ne0$. Then the …
  44. Let the circle $x^2+y^2=4$ intersect $x$-axis at the points $A(a,0)$, $a>0$ and $B(b,0)$. Let $P(2\cos\alpha,2\sin\alpha)$, $0<\alpha<\frac\pi2$ and …
  45. Tangents are drawn from the point $(17, 7)$ to the circle $x^2+y^2=169$. STATEMENT-1 : The tangents are mutually perpendicular. because STATEMENT-2 : The locus of the …
  46. If the chord $y=mx+1$ of the circle $x^{2}+y^{2}=1$ subtends an angle of measure $45^\circ$ at the major segment of the circle then value of $m$ is :
  47. Consider $L_1: 2x+3y+p-3=0$ $L_2: 2x+3y+p+3=0$, where $p$ is a real number, and $C: x^2+y^2+6x-10y+30=0$. STATEMENT-1: If line $L_1$ is a chord of circle $C$, then line …
  48. Tangents drawn from the point $P(1,8)$ to the circle $$x^2+y^2-6x-4y-11=0$$ touch the circle at the points $A$ and $B$. The equation of the circumcircle of the triangle …
  49. The circle passing through the point $(-1,0)$ and touching the $y$-axis at $(0,2)$ also passes through the point
  50. The centres of two circles $C_1$ and $C_2$ each of unit radius are at a distance of 6 units from each other. Let $P$ be the mid point of the line segment joining the …

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