NIMCET 2019 Question Paper with solutions

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Question : 29 of 120

Marks: +1, -0

Equation of the tangents from the point (3, -1) to the ellipse

2x^2 + 9y^2

= 3 is

2x-3y -3 = 0
2x + 3y-3 = 0
2x+ y - 3 = 0
None of these

Solution:

Equation of ellipse

2x^2+9y^2=3

⇒x^2/{3/2}+y^2/{1/3}=1

Here,

a=√{3/2},b=√{1/3}

Equation of tangent of ellipse is

y=mx±√{3/2m^2+1/3}

Since, this is passes through

(3,-1)

∴\;\;-1=3m±√{{9m^2+2}/6}

⇒(3m+1)^2=√{{9m^2+2}/6}

⇒6(9m^2+6m+1=9m^2+2)

⇒45m^2+36m+4=0

⇒45m^2+30m+6m++4=0

⇒(3m+2)(15m+2)=0

⇒m=-2/3

or

-2/15

∴ Equation of tangent

y={{-2}/3}x±√{2/3+1/3}

y={{-2}/3x±1

2x+3y-3=0

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