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Find the equations of the tangents to the hyperbola `x^2=9y^2=9` that are drawn from (3, 2).

Text Solution

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The equation of the hyperbola is
`(x^(2))/(9)-(y^(2))/(1)=1`
The equation of the tangent haivng slope m is
`y=mx pm sqrt(9m^(2)-1)`
It passes through (3, 2). Therefore,
`2=3m pm sqrt(9m^(2)-1)`
`"or "4+9m^(2)-12m=9m^(2)-1`
`"i.e., "m=(5)/(12)or m=oo`
Hence, the equations of the tangents are `y-3=(5)/(12)(x-2) and x=3`
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