Test Index

KEAM 2019 Math Paper

© examsnet.com

Question : 17 of 121

Marks: +1, -0

The values of

λ

for which the line

y=x+λ

touches the ellipse

9 x^{2}+16 y^{2}=144

, are

$± 3$
$± 4$
$± 5$
$± 9$
$± 11$

Solution:

Given, the equation of the line is

y=x+λ

Comparing with the standard equation of the line, we get,

m=1, c=λ

and ellipse is

\;{x^{2}}/{16}+\;{y^{2}}/{9}=1

Comparing with the standard equation of ellipse. we get,

a=± 4, b=± 3

Ifthe line touches the ellipse, then

c^{2}=a^{2} m^{2}+b^{2}

λ^{2}=16+9 \;\; \;\text " or "\; \;\; λ=± 5

© examsnet.com

Go to Question:

Prev Question

Next Question