AP EAMCET · Maths · Hyperbola
Let the points \(\mathrm{P}_1\left(\frac{\pi}{4}\right), \mathrm{P}_2\left(\frac{3 \pi}{4}\right), \mathrm{P}_3\left(\frac{5 \pi}{4}\right)\) and \(\mathrm{P}_4\left(\frac{7 \pi}{4}\right)\) given in parametric form, lie on the hyperbola \(\frac{x^2}{9}-\frac{y^2}{16}=1\). Then these four points in that order form
- A a rectangle
- B a square
- C a parallelogram
- D a rhombus
Answer & Solution
Correct Answer
(A) a rectangle
Step-by-step Solution
Detailed explanation
Since, \(\frac{x^2}{9}-\frac{y^2}{16}=1\) ...(i) \(\Rightarrow \quad a=3, b=4\) Parametric equation for hyperbola (i) is . \(x=a \sec \theta, y=b \tan \theta\) \(\Rightarrow \quad x=3 \sec \theta, y=4 \tan \theta\)…
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