JEE Main Maths · Conic Sections

Circle Tangents in JEE Main

Name: Circle Tangents: JEE Main previous year questions
Creator: Lumi

Circle Tangents (Maths, Conic Sections) came 17 times in 17 of the 42 JEE Main shifts Lumi analysed, across 10 distinct ideas. 6 of them came in 2024–26; it was last asked in 2026.

Questions: 17; in 17 shifts
Ideas asked: 10; 4 asked more than once
Numerical answer: 7; 41% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 10Hard 6

Format

Single correct10 Q
Numerical value7 Q

Ideas inside the topic

10 ideas

Family of Circles Touching a Line4 Q
Common Tangent of Touching Circles3 Q
Number of Common Tangents2 Q
Condition of tangency2 Q
Area of Tangent-Chord Triangle1 Q
Circumcircle of Tangent Triangle1 Q
Coordinates of Point of Contact1 Q
Common Tangent to Circle and Conic1 Q
Normal Passes Through Center1 Q
Tangent Parallel or Perpendicular to a Line1 Q

Where it sits

Part of Conic Sections, which had 116 questions in all. Circle Tangents accounts for 15% of them. In Lumi's JEE taxonomy it belongs to Coordinate Geometry.

Every question

All 17 Circle Tangents questions

Newest first, each with its options and official answer.

6 Apr 2026, Shift 2 · Q10Let 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…MediumSingle correct
2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point $(-9, 4)$ and touching the lines…HardNumerical value
7 Apr 2025, Shift 1 · Q12Let $C_1$ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $C_2$ be the circle with centre $(1, 3)$ …MediumSingle correct
8 Apr 2024, Shift 1 · Q15Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$ touch each other externally at…MediumSingle correct
9 Apr 2024, Shift 1 · Q29Let the centre of a circle, passing through the points $(0,0)$ , $(1,0)$ and touching the circle $x^2+y^2=9$ , be $(h,k)$ . Then for all…HardNumerical value
29 Jan 2024, Shift 1 · Q27Equations of two diameters of a circle are $2x-3y=5$ and $3x-4y=7$ . The line joining the points $\left(-\frac{22}{7},-4\right)$ and…MediumNumerical value
8 Apr 2023, Shift 2 · Q11Let $O$ 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…MediumSingle correct
13 Apr 2023, Shift 2 · Q13Let 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…MediumSingle correct
25 Jul 2022, Shift 1 · Q29The sum of diameters of the circles that touch (i) the parabola $75x^2=64(5y-3)$ at the point $\left(\frac{8}{5},\frac{6}{5}\right)$ and…HardNumerical value
24 Jun 2022, Shift 1 · Q5Let $x^2+y^2+Ax+By+C=0$ be a circle passing through $(0, 6)$ and touching the parabola $y=x^2$ at $(2, 4)$ . Then $A+C$ is equal to ______.HardSingle correct
29 Jun 2022, Shift 1 · Q19Let 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…HardSingle correct
3 Aug 2021, Shift 2 · Q86The circles, $x^2 + y^2 + 2x + 4y - 4 = 0$ and $x^2 + y^2 - 4x + 4y + k = 0$ touch each other internally. If the point of contact of these…MediumNumerical value
16 Mar 2021, Shift 2 · Q62Let 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 $2\sqrt2$ and $2\sqrt5$ ,…MediumSingle correct
18 Mar 2021, Shift 1 · Q75Choose the correct statement about two circles whose equations are given below : $x^2+y^2-10x-10y+41=0$ $x^2+y^2-22x-10y+137=0$ EasySingle correct
9 Jan 2020, Shift 2 · Q73If the curves, $x^2-6x+y^2+8=0$ and $x^2-8y+y^2+16-k=0$ , $(k>0)$ touch each other at a point, then the largest value of $k$ is ______.MediumNumerical value
2 Sep 2020, Shift 1 · Q74The number of integral values of k for which the line, $3x+4y=k$ intersects the circle, $x^{2}+y^{2}-2x-4y+4=0$ at two distinct points is…MediumNumerical value
6 Sep 2020, Shift 2 · Q65The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^2$ at the point $(2,4)$ is :HardSingle correct