# Thread: differentiation - tangent meeting another pt on y=x^3

1. ## differentiation - tangent meeting another pt on y=x^3

bk2 p41 q48
question : given the curve C: $y = x^3$ and P(h,k) is a point on C , where h and k are non-zero no.
(a)find the equation of the tangent to C at P
(b) if the tangent found in (a) intersects C again at Q , find the coordinates of Q.

my working:
$dy/dx = 3x^2$
equ. $: y= 3h^2 (x-h)+k$
sub to C
$x^3 - 3h ^2 x +3h^3 -k = 0$
don't know how to solve and find Q
thanks!

2. Never mind I cant take a derivative

3. Originally Posted by afeasfaerw23231233
bk2 p41 q48
question : given the curve C: $y = x^3$ and P(h,k) is a point on C , where h and k are non-zero no.
(a)find the equation of the tangent to C at P
(b) if the tangent found in (a) intersects C again at Q , find the coordinates of Q.

my working:
$dy/dx = 3x^2$
equ. $: y= 3h^2 (x-h)+k$
sub to C
$x^3 - 3h ^2 x +3h^3 -k = 0$
don't know how to solve and find Q
thanks!
Since P lies on C, $k = h^3$

$x^3 - 3h ^2 x +3h^3 - k = 0 \Rightarrow x^3 - 3h ^2 x +2h^3= 0$

Now since P satisfies the line as well as the curve already, h is a root of the cubic. By this and by long division:

$x^3 - 3h ^2 x +2h^3= 0 \Rightarrow (x - h)(x^2 + hx - 2h^2)= 0 \Rightarrow (x - h)^2(x+2h) = 0$

So finish it