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  • The number of values of c such that the straight line touches the curve <img alt="\frac{x^2}{4}

The number of values of c such that the straight line y=4 x+c touches the curve \frac{x^2}{4}+y^2=1, is

Option: 1

0
 


Option: 2

1
 


Option: 3

5
 


Option: 4

infinite


Answers (1)

best_answer

(c) We know that, the line y=m x+c touches the curve

\begin{array}{ll} & \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \text { iff } c^2=a^2 m^2+b^2 . \\ \\\text { Here, } & a^2=4, b^2=1, m=4 \\ \\\therefore & c^2=64+1 \Rightarrow c= \pm \sqrt{65} \end{array}
 

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Deependra Verma

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