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Find the coordinates of the point on the curve `y=x-(4)/(x)`, where the tangent is parallel to the line `y=2x`. |
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Answer» Equation of line is given by ` y = 2x ` ….(1) We know that ` y = mx + c ` …(2) On comparing equation (2) with (1), We get , m = 2 Given, ` y = x - 4/x` Differentiating w.r.t.x ` (dy)/(dx) = 1 - 4 (-1) * 1/x^(2) ` ` = 1 + 4/x^(2) = m ` ....(3) Slope of the tangent, ` m = 1 + 4/x^(2) ` ` 1 + 4/x^(2) = 2` ` x^(2) + 4 = 2x^(2)` ` x = pm 2` ` :. x_(1) = 2, x_(2) = -2` ` y_(1) = 4, y_(2) = - 4` Co- ordinates of the point of contact are (2, 4) and (-2, -4). |
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