1)

The value of λ, does the line Y = x + λ touches the ellipse 9x2 + 16y2 = 144 is/are


A) $\pm2\sqrt{2}$

B) $2\pm\sqrt{3}$

C) $\pm5$

D) $5\pm\sqrt{2}$

Answer:

Option C

Explanation:

 Equation of ellipse is 9x2 + 16y2 = 144 or  $\frac{x^{2}}{16}+\frac{y^{2}}{9} = 1$

Comparing this with $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1$

then we get a2 = 16 and b2 = 9 and comparing the line  y = x+λ, with y = mx+c

.'. m = 1 and c = λ

If the line y = x + 1, touches the eilipse 9x2 + 16y2 = 144, then c2 = a2m2+b2

→ λ2 = 16×12 +9 →  λ2 = 25 .'. λ =± 5