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A hyperbola passes through the point P(s...

A hyperbola passes through the point `P(sqrt(2),sqrt(3))` and has foci at `(+-2,0)dot` Then the tangent to this hyperbola at `P` also passes through the point :

Text Solution

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`x^2/a^2-y^2/b^2=1`
`x^2/a^2-y^2/(a^2(e^2-1))=1`
`x^2/a^2=y^2/(4-a^2)=1`
`(sqrt2)^2/a^2-(sqrt3)^2/(4-a^2)=1`
`2/a^2-3/(4-a^2)=1`
`(8-2a^2-3a^2)/(a^2(4-a^2))=1`
`8-2a^2-3a^2-4a^2+a^4=0`
Let`a^2=t`
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