Math Help - Finding eq of tangent to a parabola.

1. Finding eq of tangent to a parabola.

Find the equation of the tangent to a parabola $y^2=4ax$ at the given pt $(x_1,y_1)$ on it. What can you say about the tangent at $(0,0)$?

2. Originally Posted by varunnayudu
Find the equation of the tangent to a parabola $y^2=4ax$ at the given pt $(x_1,y_1)$ on it. What can you say about the tangent at $(0,0)$?
Just apply the definition for the first part:

$y - y_1 = \frac{dy}{dx}\bigg{|}_{x = x_1, y = y_1} (x - x_1)$
If $y_1 \neq 0, y - y_1 = \frac{2a}{y_1} (x - x_1)$
$y_1 y - y_1 ^2 = 2ax - 2ax_1$

If $y_1 = 0$, then $x_1 = 0$ and the tangent is the y - axis.

thanks man