JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A line parallel to the straight line \(2 x-y=0\) is tangent to the hyperbola \(\frac{x^{2}}{4}-\frac{y^{2}}{2}=1\) at the point \(\left(x_{1}, y_{1}\right) .\) Then \(x_{1}^{2}+5 y_{1}^{2}\) is equal to
- A \(5\)
- B \(6\)
- C \(8\)
- D \(10\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
Slope of tangent is \(2,\) Tangent of hyperbola \(\frac{x^{2}}{4}-\frac{y^{2}}{2}=1\) at the point \(\left(x_{1}, y_{1}\right)\) is \(\frac{\mathrm{xx}_{1}}{4}-\frac{\mathrm{yy}_{1}}{2}=1 \quad(\mathrm{T}=0)\) Slope…
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