JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(L\) be a common tangent line to the curves \(4 x^{2}+9 y^{2}=36\) and \((2 x)^{2}+(2 y)^{2}=31\). Then the square of the slope of the line \(L\) is ..... .
- A \(3\)
- B \(6\)
- C \(5\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
Given curves are \(\frac{ x ^{2}}{9}+\frac{ y ^{2}}{4}=1\) \(x^{2}+y^{2}=\frac{31}{4}\) let slope of common tangent be \(m\) so tangents are \(y=m x \pm \sqrt{9 m^{2}+4}\) \(y=m x \pm \frac{\sqrt{31}}{2} \sqrt{1+m^{2}}\) hence \(9 m ^{2}+4=\frac{31}{4}\left(1+ m ^{2}\right)\)…
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