TS EAMCET · Maths · Hyperbola
The lines of the form \(x \cos \phi+y \sin \phi=P\) are chords of the hyperbola \(4 x^2-y^2=4 a^2\) which subtend a right angle at the centre of the hyperbola. If these chords touch a circle with centre at \((0,0)\), then the radius of that circle is
- A \(\frac{2 a}{\sqrt{3}}\)
- B \(\frac{a}{\sqrt{3}}\)
- C \(\sqrt{2} a\)
- D \(\frac{a}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{2 a}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Since, \(x \cos \phi+y \sin \phi=P\) subtends a right angle at the centre \((0,0)\) of hyperbola \[ \Rightarrow \quad \begin{aligned} 4 x^2-y^2 & =4 a^2 \\ \frac{x^2}{a^2}-\frac{y^2}{4 a^2} & =1 \end{aligned} \] Therefore, making the hyperbola equation homogeneous with help of…
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