I have two questions for which I have partial working for, but I am unsure of the working for them.

Q)1:

Find (a) the directrix, (b) the focus and (c) the roots of the parabola $\displaystyle y=x^2-5x+4$

Answer(s):

a)

y=$\displaystyle -\frac{5}{2}$

b)

(2.5,-2)

c)

$\displaystyle y=x^2-5x+4\rightarrow y=(x-4)(x-1)$

Therefore x=4 and x=1.

I'm very certain of my answer for c), however I lost my working for a) and b) so I'm fairly certain that I am incorrect for those answers.

Q)2

Graph $\displaystyle \frac{x^2}{16}-\frac{y^2}{25}=1$

Show how you arrived at your graph by determining the x-intercepts, the extent of the graph and the asympotes.

A) I admit to being lost when it comes to this question, I know how to work these kind of questions under other situations where the x and y are reversed. E.g.: $\displaystyle \frac{y^2}{25}-\frac{x^2}{16}$. I am very lost as to what to do with this one though.

When I try to determine 'c' I come out with $\displaystyle \sqrt{41}$

I don't really see how that can be correct.

Thank you.