Question

From the point P(1, $\sqrt{2}$) on the circle x² + y² = 4 a tangent is drawn to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{1} = 1$ which meets its transverse axis 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

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

Recall the definition of parametric point on hyperbola, we have

R = $\left( 2\sec\frac{\pi}{3},1\tan\frac{\pi}{3} \right) = (4,\sqrt{3})$

∴ PR = 4 - 1 = 3.