Question

Tangent drawn to the circle at P (1,$\sqrt{3}$) on the circle x² + y² = 4. Which meets its transverse axis of hyperbola$\frac{x^{2}}{4}$–$\frac{y^{2}}{1}$=1 at Q. From Q a line is drawn parallel to conjugate axis, which cuts the hyperbola at R above the x- axis, then PR equals-

• A. 3
• B. $\sqrt{10}$
• C. $\frac{3\sqrt{3} + 4}{2}$
• D. None of these

Answer 1

Answer: (A)

3

Answer 2

$\frac{x^{2}}{4}$ – $\frac{y^{2}}{1}$ = 1

P(1, $\sqrt{3}$) ® P$\left( 2 \times \frac{1}{2},\frac{2\sqrt{3}}{2} \right)$=$\left( 2\cos\frac{\pi}{3},2\sin\frac{\pi}{2} \right)$

coordinate of Q is (2sec p/3, 0)

and coordinate of R is (2secp/3, tanp/3)

Ž R (4, $\sqrt{3}$) (using definition of parametric)

PR=$\sqrt{(4–1)^{2} + (\sqrt{3}–\sqrt{3})^{2}}$= 3