AP EAMCET · Maths · Ellipse
If \(c \in R\) be such that the line \(4 x-y+c=0\) touches the ellipse \(x^2+4 y^2=4\), then an equation having all such values of \(c\) among its roots is
- A \(x^2-(1+\sqrt{17}) x+\sqrt{17}=0\)
- B \(x^2-(1-\sqrt{17}) x-\sqrt{17}=0\)
- C \(x^3-x^2-17 x+17=0\)
- D \(x^3-x^2+17 x-17=0\)
Answer & Solution
Correct Answer
(C) \(x^3-x^2-17 x+17=0\)
Step-by-step Solution
Detailed explanation
If line \(4 x-y+c=0\) touches the ellipse \(\frac{x^2}{4}+\frac{y^2}{1}=1\), then \[ \begin{aligned} & c^2=4(4)+1 \Rightarrow c^2=17 \\ & \Rightarrow c= \pm \sqrt{17} \end{aligned} \] Now, from the options, the equation…
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