Verified Solution • 2025–26 Session moderate

QJEEM23Ma1172: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1172 Solution: Let C be the largest circle centred at (2, 0) and inscribed in…

Let C be the largest circle centred at (2, 0) and inscribed in the ellipse x236+y216=1. If (1, α) lies on C, then 10 α2 is equal to ____________

Step-by-Step Verified Solution

x236+y216=1\frac{x^{2}}{36}+\frac{y^{2}}{16}=1

r2=(x−2)2+y2r^{2}=(x-2)^{2}+y^{2}

Solving simultaneously

−5x2+36x+(9r2−180)=0-5 x^{2}+36 x+\left(9 r^{2}-180\right)=0

D=0D=0

r2=12810r^{2}=\frac{128}{10}

Distance between (1,α)(1, \alpha) and (2,0)(2,0) should be rr

1+α2=12810α2=11810=118.00

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring