With the exception of the last question, these are a tad interesting.
1) Set up parametric equations.
So you know that, by dividing by 9,
^2 +(\frac{y}{3})^2 = 1)
Knowing a tiny bit about parametric equations we can say that
)
)
Your questions asks parallel to the y, so every y point is multipled by a factor of
.
Then
)
)
So now going back from parametric to cartesian.
=
B
2) Interesting specimen with multiple solutions to it. This is by no means the most elegant.
Notice that the only thing that is of interest is the numerator of the derivative.
 = 0)
for stat points by deriving.
Subbing into the original equation.
This is the y point of the stat(s) points.
This will be undefined where the denominator = 0
Hence the stat points are undefined at
Which means option B cannot be right. This is because if we take the positive case of q, (
)
provided q is positive, then p will eventually hit 4q. This cannot happen for a stat point to exist.
Similar reasoning applies to -4q and option C.
Now option A doesn't *hit* any of these problems, and conveniently avoids -4q, so it is right.
3) The domain options are clearly wrong as they don't have fractions. This requires fractions.
4. This is relatively easy.
)
It is defined over
Cos is negative in the second quadrant. The reference angle is
But we are in the second quadrant, so
C
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