show that the equation of the line tangent to the parabola y^2 = 4ax at the point (x1, y1) is y1y= 2a (x+x1) .. PLEASE

Question

anonymous · Answer

can you use calculus?

anonymous · Answer

im so sorry but the only thing I remembered about calculus when i was in highschool was the derivation. nothing else. hehe it was just the basic of it.

anonymous · Answer

that is all you would need for this
use the derivative to get the slope
then use the point-slope formula

anonymous · Answer

take the derivative with respect to $x$  and get 
$$2yy'=4a$$ or 
$$yy'=2a$$

anonymous · Answer

solve for $y'$ which is the slope, and get $\frac{2a}{y}$
then at the point $(x_1,y_1)$ the slope will be $\frac{2a}{y_1}$

anonymous · Answer

actually maybe it would be easier to find the derivative with respect to $y$ 
either way should work

anonymous · Answer

i think i need time to review this topic again. thank you so much @satellite73 :) lifesaver!!

anonymous · Answer

yw
i am going to be that there is a non calculus way to do this, but i am not sure of what it is

anonymous · Answer

probably show that the line touches the graph at exactly one point
maybe that would do it

anonymous · Answer

yes yes!! thank you weee :)

anonymous · Answer

yw again