PrepWiser › Learn › Mathematics › CirclesCircles — JEE Main PYQs & Practice Questions Circles is a Mathematics chapter in the JEE Main syllabus. This page brings together 117 previous-year and practice questions on Circles, organised into 6 topics: Equation of a Circle, Tangent and Normal, Chord of Contact, Radical Axis, Family of Circles and Intersection of Two Circles. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Equation of a Circle Let C₁ be the circle in the third quadrant of radius 3 , that touches both coordinate… If the locus of the mid-point of the line segment from the point (3, 2) to a point on… Let P and Q be two distinct points on a circle which has center at C(2, 3) and which… The absolute difference between the squares of the radii of the two circles passing… Let the line x-y=4 intersect the circle C:(x-4)²+(y+3)²=9 at the points Q and R . If… Let the circles C₁:(x-α)²+(y-β)²=r₁² and C₂:(x-8)²+(y-15/2)²=r₂² touch each other… Let x² + y² + Ax + By + C = 0 be a circle passing through (0, 6) and touching the… If the circle x²+y²-2 g x+6 y-19 c=0, g, c ∈ ℝ passes through the point (6,1) and its… If the length of the chord of the circle, x² + y² = r² (r > 0) along the line, y – 2x =… Let the point (p, p+1) lie inside the region E={(x, y): 3-x ≤ y ≤ √(9-x²), 0 ≤ x ≤ 3}… Let the point P be the vertex of the parabola y=x²-6x+12. If a line passing through the… The number of integral values of k for which the line, 3x + 4y = k intersects the… Consider a circle C₁: x²+y²-4 x-2 y=α-5. Let its mirror image in the line y=2 x+1 be… The points of intersection of the line ax + by = 0,(a ≠ b) and the circle x² + y² - 2x =… The focus of the parabola y²=4 x+16 is the centre of the circle C of radius 5 . If the… The set of values of k, for which the circle C:4x² + 4y² - 12x + 8y + k = 0 lies inside… Let C be a circle with radius √10 units and centre at the origin. Let the line x+y=2… Let A(1, 4) and B(1, -5) be two points. Let P be a point on the circle (x - 1)² + (y -… Let a circle C : (x - h)² + (y - k)² = r², k > 0, touch the x-axis at (1, 0). If the… If the variable line 3x + 4y = α lies between the two circles (x - 1)² + (y - 1)² = 1… Tangent and Normal Points P(-3, 2), Q(9, 10) and R(α,4) lie on a circle C and PR as its diameter. The… The line 2x - y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of… Let the tangent to the circle x² + y² = 25 at the point R(3, 4) meet x-axis and y-axis… Consider a circle (x-α)²+(y-β)²=50, where α, β>0. If the circle touches the line y+x=0… If the tangents drawn at the points O(0,0) and P( 1 + √5 ,2 ) on the circle x² + y² - 2x… Two tangents are drawn from a point P to the circle x² + y² - 2x - 4y + 4 = 0, such that… Let y=x+2,4y=3x+6 and 3y=4x+1 be three tangent lines to the circle (x-h)²+(y-k)²=r²… If the area of the triangle formed by the positive x-axis, the normal and the tangent to… Let O be the origin and OP and OQ be the tangents to the circle x²+y²-6x+4y+8=0 at the… Two circles each of radius 5 units touch each other at the point (1, 2). If the equation… Let the lengths of intercepts on x-axis and y-axis made by the circle x² + y² + ax + 2ay… Let the tangents at the points A(4,-11) and B(8,-5) on the circle x²+y²-3 x+10 y-15=0… The centre of the circle passing through the point (0, 1) and touching the parabola y =… A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0)… If the tangents at the points P and Q on the circle x²+y²-2 x+y=5 meet at the point… Consider three circles: C₁:x² + y² = r² C₂:(x - 1)² + (y - 1)² = r² C₃:(x - 2)² + (y -… Let the tangent to the circle C₁ : x² + y² = 2 at the point M(-1, 1) intersect the… If a line, y = mx + c is a tangent to the circle, (x – 3)² + y² = 1 and it is… A circle C₁ passes through the origin O and has diameter 4 on the positive x-axis. The… Let the lines y + 2x = √11 + 7√7 and 2y + x = 2√11 + 6√7 be normal to a circle C:(x -… Chord of Contact Radical Axis Family of Circles Let S₁ : x² + y² = 9 and S₂ : (x - 2)² + y² = 1. Then the locus of center of a variable… Let dy/dx = (ax - by + a)/(bx + cy + a), where a, b, c are constants, represent a circle… Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the… Let a circle of radius 4 pass through the origin O , the points A(-√3a,0) and B(0,-√2b)… If the circles x² + y² + 6x + 8y + 16 = 0 and x² + y² + 2( 3 - √3 )x + 2( 4 - √6 )y = k… The circle passing through the intersection of the circles, x² + y² – 6x = 0 and x² + y²… Let the centre of a circle, passing through the points (0,0),(1,0) and touching the… Let the locus of the midpoints of the chords of the circle x²+(y-1)²=1 drawn from the… Intersection of Two Circles More Mathematics chapters Frequently asked questions How many Circles questions are there for JEE Main? PrepWiser has 117 Circles questions for JEE Main, grouped into 6 topics such as Equation of a Circle, Tangent and Normal and Chord of Contact.
Are these Circles questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Circles questions? Open any Circles question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.