KVPY SB SX Exam 2011 Question Paper

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Question : 84 of 120

Marks: +1, -0

The smallest possible positive slope of a line whose y-intercept is 5 and which has a common point with the ellipse

9x^2+16y^2=144

is

$3/4$
1
$4/3$
$9/16$

Solution:

ellipse

x^2/16+y^2/9=1

Any tangent

{x\cosθ}/4+{y\sinθ}/3=1

y intercept = 5

⇒\sinθ=3/5; θ∈(π/2,π)

⇒\cosθ=-4/5

tangent

⇒-x/5+y/5=1

⇒ slope = 1

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