Question

The line y = 2x + k is a tangent to the ellipse $\frac{x^{2}}{5}$ + y² = 1. Then k =

• A. $\sqrt{7}$
• B. $\sqrt{21}$
• C. $\sqrt{15}$
• D. $\sqrt{5}$

Answer 1

Answer: (B)

$\sqrt{21}$

Answer 2

If y = mx + c is a tangent to the ellipse, then

c² = a²m² + b²

Given m = 2, c = K, a² = 5, b² = 1

∴ K² = 5x4+1 ⇒ K = $\sqrt{21}$