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 topic in other shifts

All Circle Tangents questions

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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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.