JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Consider 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 :

y = mx + c

be a common tangent to

C_1, C_2

and

C_3

such that

C_1

and

C_3

lie on one side of line L while

C_2

lies on other side, then the value of

20(r^2 + c)

is equal to :

(1) $23$
(2) $15$
(3) $12$
(4) $6$ Official answer

Official answer

Option 4

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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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.