Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The radius of a circle having minimum area, which touches the curve     and the lines

The radius of a circle having minimum area, which touches the curve  y=4-x^2   and the lines y=|x| is

Option: 1

\begin{aligned} & 2(\sqrt{2}+1) \\ \end{aligned}


Option: 2

2(\sqrt{2}-1) \\


Option: 3

4(\sqrt{2}-1) \\


Option: 4

4(\sqrt{2}+1)


Answers (1)

best_answer

Let the radius of the circle with least area be r.

Then, then coordinates of center =(0,4-r)

Since, circle touches the line y=x  in first quadrant

\begin{aligned} & \therefore\left|\frac{0-(4-r)}{\sqrt{2}}\right|=r \\ & \Rightarrow r-4= \pm r \sqrt{2} \\ & \Rightarrow r=\frac{4}{\sqrt{2}+1} \text { or } \frac{4}{1-\sqrt{2}} \\ & \text { But, } \quad r \neq \frac{4}{1-\sqrt{2}} \\ & \therefore r=\frac{4}{\sqrt{2}+1}=4(\sqrt{2}-1) \end{aligned}

Posted by

Gunjita

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

Amrita BTech Admission 2025: JEE Main-based registration deadline extended to August 30

Latest Question