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  • The range of values of for which the circle <img alt="\mathrm{x^{2}+y^{2}=4}" src="https://entrancecorner.oncod

The range of values of \lambda for which the circle \mathrm{x^{2}+y^{2}=4} and \mathrm{x^{2}+y^{2}-4 \lambda x+9=0} have two common tangent is

Option: 1

\lambda \in\left[-\frac{13}{8}, \frac{13}{8}\right]


Option: 2

\lambda>\frac{13}{8}$ or $\lambda<\frac{13}{8}


Option: 3

k \lambda<\frac{13}{8}


Option: 4

none


Answers (1)

best_answer

Solving the equation \mathrm{4-4 \lambda x+9=0 \Rightarrow x=\frac{13}{4 \lambda}}

\mathrm{\Rightarrow x^{2}+\left(\frac{13}{4 \lambda}\right)^{2}=4 \text { or } x= \pm \sqrt{4-\left(\frac{13}{4 \lambda}\right)^{2}} }. It should have two real and

distinct values so \mathrm{4-\left(\frac{13}{4 \lambda}\right)^{2}>0 \Rightarrow \lambda \in\left(-\frac{13}{8},-\frac{13}{8}\right)}

Hence (A) is the correct answer.

Posted by

sudhir.kumar

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