Question

The line $y=x+\lambda$ is tangent to the ellipse $2x^2+3y^2=1.$ Then $\lambda$ is

• A. $-2$
• B. $1$
• C. $\sqrt{\frac{5}{6}}$
• D. $\sqrt{\frac{2}{3}}$

Answer 1

The correct option is C $\sqrt{\frac{5}{6}}$

The line $y=x+\lambda$ is tangent to the ellipse $2x^2+3y^2=1.$
So,
${\lambda }^2=a^2{m}^2+b^2{\lambda }^2=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\Rightarrow \lambda =\sqrt{\frac{5}{6}}$