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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let a circle C touch the lines L1\mathrm{L_1} : 4x−3y+K1=04x-3y+K_1=0 and L2\mathrm{L_2} : 4x−3y+K2=04x-3y+K_2=0, K1,K2∈RK_1, K_2 \in \mathbf{R}. If a line passing through the centre of the circle C intersects L1\mathrm{L_1} at (−1,2)(-1, 2) and L2\mathrm{L_2} at (3,−6)(3, -6), then the equation of the circle C is :
  1. (1)(x−1)2+(y−2)2=4(x-1)^2+(y-2)^2=4
  2. (2)(x+1)2+(y−2)2=4(x+1)^2+(y-2)^2=4
  3. (3)(x−1)2+(y+2)2=16(x-1)^2+(y+2)^2=16Official answer
  4. (4)(x−1)2+(y−2)2=16(x-1)^2+(y-2)^2=16

Official answer

Option 3

NTA final key.

Chapter
Conic Sections
Topic
Circle Tangents
Idea tested
Family of Circles Touching a Line

Same idea in other shifts

Asked 8× in all
  1. 6 Apr 2026, Shift 2 · Q10Let C be a circle having centre in the first quadrant and touching the xx-axis at a distance of 3 units from the origin. If the circle C…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point (−9,4)(-9, 4) and touching the lines…HardNumerical value
  3. 25 Jul 2022, Shift 1 · Q29The sum of diameters of the circles that touch (i) the parabola 75x2=64(5y−3)75x^2=64(5y-3) at the point (85,65)\left(\frac{8}{5},\frac{6}{5}\right) and…HardNumerical value
  4. 24 Jun 2022, Shift 2 · Q27Let a circle C:(x−h)2+(y−k)2=r2C : (x-h)^2 + (y-k)^2 = r^2, k>0k > 0, touch the xx-axis at (1,0)(1, 0). If the line x+y=0x + y = 0 intersects the circle CC at…MediumNumerical value
  5. 4 Aug 2021, Shift 1 · Q73Consider a family of circles which pass through the point (1,1)(1, 1) and touch the axis of yy. If the centre of such a circle is at…MediumSingle correct
  6. 26 Aug 2021, Shift 2 · Q71A circle C touches the line x=2yx=2y at the point (2, 1)(2,\ 1) and intersects the circle C1:x2+y2+2y−5=0C_1:x^2+y^2+2y-5=0 at two points P and Q such that…HardSingle correct
  7. 6 Sep 2020, Shift 2 · Q65The centre of the circle passing through the point (0,1)(0,1) and touching the parabola y=x2y=x^2 at the point (2,4)(2,4) is :HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.