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If the variable line y=k x+2h is tangent...

If the variable line `y=k x+2h` is tangent to an ellipse `2x^2+3y^2=6,` then the locus of `P(h ,k)` is a conic `C` whose eccentricity is `3.` Then the value of `3e^2` is___________

Text Solution

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By using the condition of tanegency, we get `4h^(2)=3k^(2)+2`
Therrfore, the locus of P(,k) is `4x^(2)-3y^(2)=2` (which is hyperbola). Hene,
`e^(2)=1+(4)/(3) or e=sqrt((7)/(3))`
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