Question

The line \(y=x+\lambda\) is tangent to the ellipse \(2 x^{2}+3 y^{2}=1\). Then \(\lambda\) is
(A) \(-2\)
(B) 1
(C) \(\sqrt{\frac{5}{6}}\)
(D) \(\sqrt{\frac{2}{3}}\)

Answer 1

Ans : (C)
 \(: \lambda^{2}=\frac{1}{2}+\frac{1}{3}=5 / 6 \Rightarrow \lambda=\sqrt{5 / 6}\)