JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A tangent line \(\mathrm{L}\) is drawn at the point \((2,-4)\) on the parabola \(\mathrm{y}^{2}=8 \mathrm{x}\). If the line \(\mathrm{L}\) is also tangent to the circle \(x^{2}+y^{2}=a\), then \('a'\) is equal to .... .
- A \(9\)
- B \(3\)
- C \(4\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
tangent of \(y^{2}=8 x\) is \(y=m x+\frac{2}{m}\) \(\mathrm{P}(2,-4) \Rightarrow-4=2 \mathrm{~m}+\frac{2}{\mathrm{~m}}\) \(\Rightarrow \mathrm{m}+\frac{1}{\mathrm{~m}}=-2 \Rightarrow \mathrm{m}=-1\) \(\therefore\) tangent is \(\mathrm{y}=-\mathrm{x}-2\)…
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