Question

If tangents drawn to the ellipse through point (1, 2$\sqrt{3}$) to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{b^{2}} = 1$ are at right angle, then value of b is

• A. 1
• B. 4
• C. 2
• D. None of these

Answer 1

Answer: (C)

2

Answer 2

Since tangents drawn from (1, 2$\sqrt{3}$) to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{b^{2}} = 1$ are right angles, therefore, (1, 2$\sqrt{3}$) will be on the director circle of the ellipse, i.e. (1, 2$\sqrt{3}$) will lie on x² + y² = 9 + b²

∴ 13 = 9 + b² ⇒ b² = 4 ⇒ b = 2