Let the mirror image of a circle $c_1 : x^2 + y^2 - 2x - 6y + \alpha = 0$ in line $y = x + 1$ be $c_2 : 5x^2 + 5y^2 + 10gx + 10fy + 38 = 0$. If r is the radius of circle $c_2$, then $\alpha + 6r^2$ is equal to __________.

JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q30

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

Let the mirror image of a circle

c_1 : x^2 + y^2 - 2x - 6y + \alpha = 0

in line

y = x + 1

c_2 : 5x^2 + 5y^2 + 10gx + 10fy + 38 = 0

. If r is the radius of circle

c_2

, then

\alpha + 6r^2

is equal to __________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Reflection of Center Across Tangent

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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.