JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If two tangents drawn from a point \((\alpha, \beta)\) lying on the ellipse \(25 x^{2}+4 y^{2}=1\) to the parabola \(y^{2}=4 x\) are such that the slope of one tangent is four times the other, then the value of \((10 \alpha+5)^{2}+\left(16 \beta^{2}+50\right)^{2}\) equals
- A \(7982\)
- B \(2898\)
- C \(2929\)
- D \(3289\)
Answer & Solution
Correct Answer
(C) \(2929\)
Step-by-step Solution
Detailed explanation
\(\alpha=\frac{1}{5} \cos \theta, \beta=\frac{1}{2} \sin \theta\) Equation of tangent to \(y ^{2}=4 x\) \(y = mx +\frac{1}{ m }\) It passes through \((\alpha, \beta)\) \(\frac{1}{2} \sin \theta=m \frac{1}{5} \cos \theta+\frac{1}{m}\)…
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