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The line `y = m x + 1`is a tangent to the curve `y^2=4x`if the value of m is(A) 1 (B) 2 (C) 3 (D) `1/2`A. 1B. 2C. 3D. `1/2` |
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Answer» Correct Answer - A Equation of tangent on the curve is `y=mx+1`. `:." Given curve "y^(2)=4x` ` rArr 2y(dy)/(dx) = 4 rArr (dy)/(dx) = 2/y` If the tangent of the curve is `y=mx + 1" then "2/y = m` ` rArr y = 2/m` put the value of y in equation (1), ` x = y^(2)/4 = 1/4 (2/m)^(2) = 1/m^(2)` `:. ` The point will satisfy the line `y=mx + 1` `:. 2/m = m(1/m^(2))+1 rArr 1/m = 1 rArr m = 1` |
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