First slide

Parabola

Question

If a tangent to the parabola $y^{2} = 4 x$ makes an angle
$π / 4$ with the positive direction of the axis of $x$ ,
then the coordinates of the point of contact with
the parabola are:

Moderate

A

(1, 2)
B

(1, –2)
C

(4, 4)
D

(4, –4)

Solution

Slope of the tangent to the parabola at $(t^{2}, 2 t)$ is
$\frac{1}{t} = \tan \frac{π}{4} = 1 \Rightarrow t = 1$ nd the required point of
contact is (1, 2).

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