TS EAMCET · Maths · Hyperbola
Assertion : The distance between the points \(p\left(\frac{\pi}{4}\right)\) and \(p\left(\frac{\pi}{3}\right)\) on the hyperbola \(9 x^2+16 y^2=9\) is \[ \frac{1}{2 \sqrt{2}} \sqrt{66-33 \sqrt{2}-9 \sqrt{3}} \] Reason : \(x=a \cosh t, y=b \sin \mathrm{h} t\) are the parametric equations of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) The correct option among the following is
- A (A) is true, (R) is true and (R) is the correct explanation for (A)
- B (A) is true, (R) is true but (R) is not the correct explanation for (A)
- C (A) is true but (R) is false
- D (A) is false but (R) is true
Answer & Solution
Correct Answer
(C) (A) is true but (R) is false
Step-by-step Solution
Detailed explanation
Given equation of hyper bola is \(9 x^2+16 y^2=9\) which is not in the standard form of hyper bola. Equation of hyperbola should be \(9 x^2-16 y^2=9\) \(\frac{x^2}{(1)^2}-\frac{y^2}{\left(\frac{3}{4}\right)^2}=1\) So, \(a=1\) and \(b=\frac{3}{4}\).…
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