JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Consider a hyperbola \(\mathrm{H}\) having centre at the origin and foci and the \(\mathrm{x}\)-axis. Let \(\mathrm{C}_1\) be the circle touching the hyperbola \(\mathrm{H}\) and having the centre at the origin. Let \(\mathrm{C}_2\) be the circle touching the hyperbola \(\mathrm{H}\) at its vertex and having the centre at one of its foci. If areas (in sq. units) of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) are \(36 \pi\) and \(4 \pi\), respectively, then the length (in units) of latus rectum of \(\mathrm{H}\) is :
- A \(\frac{28}{3}\)
- B \(\frac{14}{3}\)
- C \(\frac{10}{3}\)
- D \(\frac{11}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{28}{3}\)
Step-by-step Solution
Detailed explanation
\( \text { Let } \mathrm{H}: \frac{\mathrm{x}^2}{\mathrm{a}^2}-\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1 \quad\left(\mathrm{~b}^2=\mathrm{a}^2\left(\mathrm{e}^2-1\right)\right) \)…
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