Find the equation(s) of the tangent line(s) to the parabola y=x^2 throught the given point: (a) (0,a) and (b) (a,0)

Question

anonymous · Answer

Well.. It's pretty hard to understand it the way you wrote it, but this is how I understand it:

Assuming we have the following function:
$$
f(x) = x^2
$$
We have to points
$$
a \to (0,a) \
b \to (b, 0)
$$
to find a and b we have to use the other part of the coordinates
$$
a \to (0,a) \
f(0) = 0^0 = 0\
a \to (0,0)
\;\\;\
b \to(b,0)\
f(x) = 0 \
x^2 = 0 \
x = 0 \
b \to (0, 0)
$$
Since they both are same point then

Using derivative
$$
f'(x) = 2x \
f'(0) = 2 \cdot 0 = 0
$$
We have a slope 0 tangent line at (0,0) which makes it
$$
y = 0 \cdot x + 0 = 0
$$
Hope I got it right