If the tangent at the point $(16,64)$ on the curve $y^2=x^3$ meets the curve again at at $Q(u,v)$ then $uv$ is ?
If found the tangent to the curve at $(16,64)$ but then I cannot find $uv$.Give your suggestions please.
[Math] Tangent meets curve again
calculusderivatives
Best Answer
We have $$y^2 = x^3.$$
Differentiate both sides, $$2yy^{(1)} = 3x^{2}.$$
put (16, 64) into it, the tangent line is $$y = 6x-32.$$
put $y = 6x- 32$ into $y^2 = x^3$, we get two coordinate $$(x, y) = (16, 64), (4, -8)$$
the Q(u, v) should be (4, -8).