A tangent to the parabola y^{2}=4x is inclined at an angle 45^{\circ} with the positive direction of x-axis. What is the point of contact of the tangent and the parabola?

Explanation

For the parabola y^2 = 4ax, a=1. The slope of the tangent is m = \tan 45^{\circ} = 1. The point of contact for a tangent of slope m to y^2 = 4ax is given by (a/m^2, 2a/m). Substituting a=1, m=1 gives (1/1^2, 2(1)/1) = (1,2).

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