SOLUTION: A tangent to the parabola x2 = 4ay is inclined at an angle with the x-axis,find then coordinates of point of contact

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Question 1024736: A tangent to the parabola x2 = 4ay is inclined at an angle with the x-axis,find then coordinates of point of contact
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2=4ay, or a better form with which to work, y=%281%2F%284a%29%29x%5E2. The line or lines tangent to the parabola will have slope dy%2Fdx=%281%2F%284a%29%29%2A2x=%281%2F%282a%29%29x.

Any general point on the parabola is (x, (x^2)/(4a)).
Pick any of these points you like as long as x%3C%3E0. Why? Because at x=0, the slope is 0, for a horizontal line, and will not make an angle with the x-axis. The question description specifies that the tangent line makes an angle with the x-axis.