JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 1 February 2024, Shift 1, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let the line

L:\sqrt{2}x+y=\alpha

pass through the point of the intersection P (in the first quadrant) of the circle

x^2+y^2=3

and the parabola

x^2=2y

. Let the line L touch two circles

C_1

and

C_2

of equal radius

2\sqrt{3}

. If the centres

Q_1

and

Q_2

of the circles

C_1

and

C_2

lie on the y-axis, then the square of the area of the triangle

PQ_1Q_2

is equal to __________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Condition of tangency

Same idea in other shifts

Asked 11× in all

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30 Jun 2022, Shift 1 · Q14Consider three circles : $C_1 : x^2 + y^2 = r^2$ $C_2 : (x-1)^2 + (y-1)^2 = r^2$ $C_3 : (x-2)^2 + (y-1)^2 = r^2$ If a line L :…HardSingle correct
31 Aug 2021, Shift 1 · Q86If the variable line $3x+4y=\alpha$ lies between the two circles $(x-1)^2+(y-1)^2=1$ and $(x-9)^2+(y-1)^2=4$ , without intercepting a chord…HardNumerical value
8 Jan 2020, Shift 2 · Q64If a line, $y = mx + \mathrm{c}$ is a tangent to the circle, $(x - 3)^2 + y^2 = 1$ and it is perpendicular to a line $\mathrm{L}_1$ , where…MediumSingle correct
9 Jan 2020, Shift 1 · Q65A circle touches the $y$ -axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to…MediumSingle correct
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

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.