Q74 / 180 · KCET 2009 · Mathematics

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

  • A
    1
  • Correct answer
    B
    2
  • C
    $\infty$
  • D
    0

Solution

Given, $\mathrm{y}=4 \mathrm{x}+\mathrm{c}$ and $\frac{\mathrm{x}^{2}}{4}+\mathrm{y}^{2}=1$ Condition for tangency, $$ \begin{array}{ll} & c^{2}=a^{2} m^{2}+b^{2} \\ \therefore & c^{2}=4(4)^{2}+1^{2} \\ \Rightarrow & c^{2}=65 \\ \Rightarrow & c=\pm \sqrt{65} \end{array} $$ Hence, for two values of c, the line touches the curve.

Hence, the correct answer is option: 'B'.

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