Question

The minimum distance between the circle x² + y² = 9 and the curve 2x² + 10y² + 6xy =1 is

• A. 2$\sqrt{2}$
• B. 2
• C. 3 –$\sqrt{2}$
• D. 3 –$\frac{1}{\sqrt{11}}$

Answer 1

Answer: (B)

2

Answer 2

Let (r cos θ, r sin θ) be any point on the curve

2x² + 10y² + 6xy =1

then 2r² cos²θ + 10r² sin²θ + 6r²sin θ cos θ = 1

r² = $\frac{1}{2 + 8\sin^{2}\theta + 3\sin 2\theta}$=

$\frac{1}{6 + 3\sin 2\theta + 4\sin 2\theta}$⇒ r_max = 1

minimum distance between curve = 2.