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VITEEE 2018 Paper

Section: Mathematics

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Question : 110 of 125

Marks: +1, -0

The value of λ does the line y = x + λ touches the ellipse

9x^2+16y^2

= 144 is/are

± $2\sqrt{2}$
2 ± $\sqrt{3}$
± 5
5 ± $\sqrt{2}$

Solution:

Since Equation of ellipse is

9x^2+16y^2

= 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

a^2

= 16 and

b^2

= 9 and comparing the line

y = x + λ with y = mx + c

∴ m = 1 and c = A,

If the line y = x + λ, touches the ellipse

9x^2 + 16y^2

= 144, then

c^2

=

a^2m^2

+

b^2

⇒

\lambda^2

= 16 x

1^2

+ 9 ⇒

\lambda^2

= 25

∴ λ = ± 5

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