JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If a tangent to the ellipse \(x^{2}+4 y^{2}=4\) meets the tangents at the extremities of its major axis at \(\mathrm{B}\) and \(\mathrm{C}\), then the circle with \(\mathrm{BC}\) as diameter passes through the point:
- A \((-1,1)\)
- B \((1,1)\)
- C \((\sqrt{3}, 0)\)
- D \((\sqrt{2}, 0)\)
Answer & Solution
Correct Answer
(C) \((\sqrt{3}, 0)\)
Step-by-step Solution
Detailed explanation
\(\frac{x^{2}}{4}+\frac{y^{2}}{1}=1 \Rightarrow a=2 \& b=1, \quad\) Let \(P(2 \cos \theta, \sin \theta)\) Equation of tangent at \(P\) is \((\cos \theta) x+2 \sin \theta y=2\) \(\mathrm{B}\left(-2, \frac{1+\cos \theta}{\sin \theta}\right)\)…
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