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JEE Advanced 2021 Paper 2

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Consider the region

R=\{(x,y)\in\mathbb{R}\times\mathbb{R}: x\ge 0

and

y^{2}\le 4-x\} .

Let

F

be the family of all circles that are contained in

R

and have centers on the

x

-axis. Let

C

be the circle that has largest radius among the circles in

F

. Let

(\alpha, \beta)

be a point where the circle

C

meets the curve

y^{2}=4-x

Section: Mathematics

Question : 46 of 57

Marks: +1, -0

The value of

\alpha

Solution:

For point of intersection.

Put

\lambda = -3

in equation (i)

x^{2} - 4x + 4 = 0 \Rightarrow x = 2

\alpha = 2

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