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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 101-150 of 305

  1. Let the straight line $y=2x$ touch a circle with center $(0,\alpha)$, $\alpha>0$, and radius $r$ at a point $A_1$. Let $B_1$ be the point on the circle such that the …
  2. Consider a circle $(x-\alpha)^2+(y-\beta)^2=50$, where $\alpha,\beta>0$. If the circle touches the line $y+x=0$ at the point $P$, whose distance from the origin is …
  3. Let $P$ be the point on the parabola $y=x^2$ such that the slope of the tangent to the parabola at the point $P$ is $4$. Let $Q$ be the point in the first quadrant lying …
  4. Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I (P) The circle with centre $(1,2)$ and touching the straight line …
  5. Let the point $B$ be the reflection of the point $A(2,3)$ with respect to the line $8x-6y-23=0$. Let $\Gamma_A$ and $\Gamma_B$ be circles of radii 2 and 1 with centres …
  6. Let the centre of the circle $x^{2}+y^{2}+2gx+2fy+25=0$ be in the first quadrant and lie on the line $2x-y=4$. Let the area of an equilateral triangle inscribed in the …
  7. Points $P(-3,2)$, $Q(9,10)$ and $R(\alpha,4)$ lie on a circle $C$ with $PR$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If …
  8. The points of intersection of the line $4x-3y-10=0$ and the circle $x^{2}+y^{2}-2x+4y-20=0$ are ______ and ______.
  9. Let circle $C$ be the image of $x^{2}+y^{2}-2x+4y-4=0$ in the line $2x-3y+5=0$ and $A$ be the point on $C$ such that $OA$ is parallel to $x$-axis and $A$ lies on the …
  10. A triangle is formed by the tangents at the point $(2,2)$ on the curves $y^{2}=2x$ and $x^{2}+y^{2}=4x$, and the line $x+y+2=0$. If $r$ is the radius of its …
  11. The equation of the circle passing through $(1,1)$ and the points of intersection of $x^{2}+y^{2}+13x-3y=0$ and $2x^{2}+2y^{2}+4x-7y-25=0$ is
  12. Find the equation of the circle whose radius is $5$ and which touches the circle $x^{2}+y^{2}-2x-4y-20=0$ at the point $(5,5)$.
  13. Let $C_1$ be the circle of radius $1$ with center at the origin. Let $C_2$ be the circle of radius $r$ with center at the point $A=(4,1)$, where $1<r<3$. Two distinct …
  14. Let a circle $C$ pass through the points $(4,2)$ and $(0,2)$, and its centre lie on $3x+2y+2=0$. Then the length of the chord, of the circle $C$, whose mid-point is …
  15. The set of all values of $a^{2}$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P\left(\frac{1+a}{2},\frac{1-a}{2}\right)$ on the circle …
  16. A square is inscribed in the circle $x^{2}+y^{2}-2x+4y+3=0$. Its sides are parallel to the coordinate axes. Then one vertex of the square is
  17. The centre of the circle passing through the point $(0,1)$ and touching the curve $y=x^{2}$ at $(2,4)$ is
  18. If $A$ and $B$ are points in the plane such that $PA/PB=k$ (constant) for all $P$ on a given circle, then the value of $k$ cannot be equal to ______.
  19. Two circles $x^{2}+y^{2}=6$ and $x^{2}+y^{2}-6x+8=0$ are given. Then the equation of the circle through their points of intersection and the point $(1,1)$ is
  20. Let $A$ be the centre of the circle $x^{2}+y^{2}-2x-4y-20=0$. Suppose that the tangents at the points $B(1,7)$ and $D(4,-2)$ on the circle meet at the point $C$. Find …
  21. If a circle $C$ passing through $(4,0)$ touches the circle $x^{2}+y^{2}+4x-6y-12=0$ externally at a point $(1,-1)$, then the radius of the circle $C$ is :
  22. If each of the lines $5x+8y=13$ and $4x-y=3$ contains a diameter of the circle $x^{2}+y^{2}-2\left(a^{2}-7a+11\right)x-2\left(a^{2}-6a+6\right)y+b^{3}+1=0$, then :
  23. If two vertices of an equilateral triangle are $A(-a,0)$ and $B(a,0)$, $a>0$, and the third vertex $C$ lies above $x$-axis then the equation of the circumcircle of …
  24. The straight line $x+2y=1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A$, $B$ and the origin. Then the sum of perpendicular distances from $A$ …
  25. Two circles with equal radii are intersecting at the points $(0,1)$ and $(0,-1)$. The tangent at the point $(0,1)$ to one of the circles passes through the centre of the …
  26. The line $x=y$ touches a circle at the point $(1,1)$. If the circle also passes through the point $(1,-3)$, then its radius is
  27. If the area of an equilateral triangle inscribed in the circle $x^2+y^2+10x+12y+c=0$ is $27\sqrt3$ sq. units, then $c$ is equal to :
  28. The centres of those circles which touch the circle $x^{2}+y^{2}-8x-8y-4=0$ externally and also touch the $x$-axis, lie on
  29. The tangent to the circle $C_1: x^{2}+y^{2}-2x-1=0$ at the point $(2,1)$ cuts off a chord of length $4$ from a circle $C_2$ whose centre is $(3,-2)$. The radius of $C_2$ …
  30. Let the tangents drawn to the circle $x^2+y^2=16$ from the point $P(0,h)$ meet the $x$-axis at points $A$ and $B$. If the area of $\Delta APB$ is minimum, then the …
  31. Let the tangents drawn from the origin to the circle $x^2+y^2-8x-4y+16=0$ touch it at the points $A$ and $B$. Then $(AB)^2$ is equal to :
  32. If the tangent to the conic $y-6=x^2$ at $(2,10)$ touches the circle $x^2+y^2+8x-2y=k$ (for some fixed $k$) at a point $(\alpha,\beta)$; then $(\alpha,\beta)$ is
  33. The points of intersection of the line $ax+by=0,\ (a\neq b)$ and the circle $x^{2}+y^{2}-2x=0$ are $A(\alpha,0)$ and $B(1,\beta)$. The image of the circle with $AB$ as a …
  34. If a circle passing through the point $(-1,0)$ touches $y$-axis at $(0,2)$, then the $x$-intercept of the circle is
  35. If $y+3x=0$ is the equation of a chord of the circle $x^2+y^2-30x=0$, then the equation of the circle with this chord as diameter is :
  36. If one of the diameters of the circle given by the equation $x^{2}+y^{2}-4x+6y-12=0$ is a chord of a circle $S$, whose centre is at $(-3,2)$, then the radius of $S$ is
  37. A square is inscribed in the circle $x^{2}+y^{2}-6x+8y-103=0$ with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is …
  38. Let the tangents at the points $A(4,-11)$ and $B(8,-5)$ on the circle $x^{2}+y^{2}-3x+10y-15=0$, intersect at the point $C$. Then the radius of the circle, whose centre …
  39. Three circles of radii $a$, $b$, $c$ ($a<b<c$) touch each other externally. If they have $x$-axis as a common tangent, then:
  40. If the angle of intersection at a point where the two circles with radii $5$ cm and $12$ cm intersect is $90^\circ$, then the length (in cm) of their common chord is:
  41. If the circles $x^{2}+y^{2}-16x-20y+164=r^{2}$ and $(x-4)^{2}+(y-7)^{2}=36$ intersect at two distinct points, then :
  42. If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16x+12y+c=0$ then the value of $c$ is:
  43. Let the line $x+y=1$ meet the circle $x^2+y^2=4$ at the points $A$ and $B$. If the line perpendicular to $AB$ and passing through the mid point of the chord $AB$ …
  44. If a variable line $3x+4y-\lambda=0$ is such that the two circles $x^{2}+y^{2}-2x-2y+1=0$ and $x^{2}+y^{2}-18x-2y+78=0$ are on its opposite sides, then the set of all …
  45. The locus of the centres of the circles, which touch the circle $x^{2}+y^{2}=1$ externally, also touch the $y$-axis and lie in the first quadrant, is :
  46. A circle touching the $x$-axis at $(3,0)$ and making an intercept of length $8$ on the $y$-axis passes through the point :
  47. Let $C_1$ and $C_2$ be the centres of the circles $x^{2}+y^{2}-2x-2y-2=0$ and $x^{2}+y^{2}-6x-6y+14=0$ respectively. If $P$ and $Q$ are the points of intersection of …
  48. If a circle $C$, whose radius is $3$, touches externally the circle $x^{2}+y^{2}+2x-4y-4=0$ at the point $(2,2)$, then the length of the intercept cut by this circle $C$ …
  49. A circle passes through $(-2,4)$ and touches the $y$-axis at $(0,2)$. Which one of the following equations can represent a diameter of this circle ?
  50. If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$, then the locus of the foot of perpendicular from $O$ on $AB$ …

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