Question

Find an equation in x and y for the line tangent to the curve x(t) = 4t², y(t) = t⁴ at the point (10,16).
A) y - 16 = 4(x - 10)
B) y = 4x - 10
C) y = 16x - 10
D) y = 4x + 10

Answer 1

first, you are wrong when you say
x(t) = 4t² gives us 4t² = 10, so t = √(10/4) = √2
in fact, t = √(5/2)
However, we also need y(t) = 16, so t^4 = 16, making t=2.
So, the point (10,16) is not on the curve at all!