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The line 3x-4y = 12 is a tangent to the ...

The line `3x-4y = 12` is a tangent to the ellipse with foci (-2, 3) and (-1, 0). Find the eccentricity of the ellipse.

Text Solution

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`f1(-2,3) & f2(-1,0)`
So, `2ae=sqrt((-2+1)^2+ (3-0)^2)=sqrt10` `4a^2e^2=10`
`a^2*(1-b^2/a^2)=5/2`
So, `a^2-b^2=5/2`
Equation of tangent,`y=(3x)/4-3`
&
`y=mx pmsqrt(a^2m^2 +b^2)`
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