JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 July 2022, Shift 2, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

If the circles

x^2+y^2+6x+8y+16=0

and

x^2+y^2+2\left(3-\sqrt{3}\right)x+2\left(4-\sqrt{6}\right)y=k+6\sqrt{3}+8\sqrt{6},\ k>0

, touch internally at the point

P(\alpha,\beta)

, then

\left(\alpha+\sqrt{3}\right)^2+\left(\beta+\sqrt{6}\right)^2

is equal to ___________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Common Tangent of Touching Circles

Same idea in other shifts

Asked 5× in all

7 Apr 2025, Shift 1 · Q12Let $C_1$ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $C_2$ be the circle with centre $(1, 3)$ …MediumSingle correct
8 Apr 2024, Shift 1 · Q15Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$ touch each other externally at…MediumSingle correct
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
27 Aug 2021, Shift 2 · Q85Two circles each of radius 5 units touch each other at the point $(1, 2)$ . If the equation of their common tangent is $4x + 3y = 10$ , 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 108 of the 174 JEE Main shifts held from 2017 to 2026.