JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 13 April 2023, Shift 2, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let 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 normal to C. Then

(\alpha-\beta+r)

is equal to

(1) $5$
(2) $6$
(3) $7$ Official answer
(4) $9$

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Normal Passes Through Center

Same idea in other shifts

Asked 4× in all

28 Jun 2022, Shift 1 · Q30Let the lines $y+2x=\sqrt{11}+7\sqrt{7}$ and $2y+x=2\sqrt{11}+6\sqrt{7}$ be normal to a circle $C:(x-h)^2+(y-k)^2=r^2$ . If the line…HardNumerical value
25 Feb 2021, Shift 1 · Q62Let the lines $(2-i)z = (2+i)\bar{z}$ and $(2+i)z + (i-2)\bar{z} - 4i = 0$ , (here $i^2 = -1$ ) be normal to a circle C. If the line…HardSingle correct
17 Mar 2021, Shift 1 · Q74The line $2x-y+1=0$ is a tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x-2y=4$ . Then, the radius of…MediumSingle 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.