NIMCET 2014 Question Paper with solutions

Question : 42 of 120

Marks: +1, -0

The condition that the line lx + my + n = 0 becomes a tangent to the ellipse

x^2/a^2+y^2/b^2

= 1 , is

Solution:

We have equation of line,
lx + my + nz = 0
and y =

{-l}/m

x +

({-n}/m)

z ... (i)
We know that, if the line y = mx + c touches the ellipse

x^2/a^2+y^2/b^2

= 1
Then ,

c^2

a^2m^2

b^2

∴

n^2/m^2

a^2 l^2/m^2

b^2

⇒

n^2

a^2l^2+b^2m^2

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