Mathematics | VITEEE 2018 | Discussion Page

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) $5\pm\sqrt{2}$

Option C

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

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