Question

The product of the slopes of the tangents to the ellipse 2x²+3y²=6 drawn from the point (1,2) is

• A. 1
• B. 2
• C. -1
• D. –2

Answer 1

Answer: (A)

1

Answer 2

If the tangents are drawn from (x₁, y₁) to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, then their slopes are obtained from

m²($x_{1}^{2} - a^{2}$) – 2mx₁y₁ + ($y_{1}^{2} - b^{2})$ =0.

⇒ m²(1 –3) – 2mx1x2 + (4 – 2) = 0

⇒ 2m² + 4m – 2 = 0

⇒ m² + 2m – 1 = 0

⇒ ∴ product of the slopes = product of roots = 1