The point of contact of the line y = x - 1 wi | vedclass

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Question

(a) The equation of the line and hyperbola are

$y = x - 1$.....$(i)$

$3{x^2} - 4{y^2} = 12$.....$(ii)$

From $(i)$ and $(ii),$ we get

$3{x^

Vedclass · Accepted Answer

$(4, 3)$

Vedclass · Answer

(a) The equation of the line and hyperbola are

$y = x - 1$.....$(i)$

$3{x^2} - 4{y^2} = 12$.....$(ii)$

From $(i)$ and $(ii),$ we get

$3{x^2} - 4{(x - 1)^2} = 12$

$ \Rightarrow 3{x^2} - 4({x^2} - 2x + 1) = 12$

or ${x^2} - 8x + 16 = 0$

$&rArr;$ $x = 4$

From $(i),$ $y = 3.$

So point of contact is $(4,3)$.

The point of contact of the line $y = x - 1$ with $3{x^2} - 4{y^2} = 12$ is

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