Melody

with the minus sign

$$\begin{array}{rll}
x^2+3x+y^2-17 &=& 0\\\\
x^2+3x+y^2 &=& 17\\\\
x^2+3x+(\frac{3}{2})^2\;\;+y^2 &=& 17+(\frac{3}{2})^2\\\\
(x+\frac{3}{2})^2\;\;+y^2 &=& 17+\frac{9}{4}\\\\
(x+\frac{3}{2})^2\;\;+y^2 &=& \frac{77}{4}\\\\
(x+\frac{3}{2})^2\;\;+y^2 &=& \left(\frac{\sqrt{77}}{2}\right)^2\\\\
\end{array}\\\\
centre\;\;(\frac{-3}{2},\;0)\qquad radius&=& \frac{\sqrt{77}}{2}$$

This one has a focal length of 314/2 = 157

and it i concave up since the directrix is below the vertex.

so      $$a=157$$

$$\\x^2=4ay\\\\
x^2=4*157y\\\\
x^2=628y$$

$$\\(x-h)^2=4a(y-k) \qquad where \;\;h=0\;\;and\;\;k=0\\\\
x^2=4ay\\\\
$The directric is above the vertex so the parabola is concave down$\\
$so a is negaive$\\\\
a=-1/22\\\\\\
x^2=\frac{-4y}{22}\\\\
x^2=\frac{-2y}{11}\\\\
or\\\\
11x^2+2y=0$$

Thanks Dragonlance :)

It appears anon that your answer is 1000 times too big.

If you were a physicist this would be a big error but for a maths exercise it is only a little error.  :)

So three points for both of you   :))

You do not have to appologize to me MG.

I am very proud of you and I know that you try very hard.

If you are really busy with school or something else then just let me know and I will know not to push so hard.

Sometimes I get too pushy, I know that :))

You should do very well at maths.  

Just be super careful because you do tend to make a lot of careless mistakes.

I expect that your knowledge base is excellent :))

I am sure that you work really hard at your other subject as well so you will do well in those exams too :)

Having said all that is there any maths topics that you would like me to look at with you?

I mean ones that relate to Monday's exam?

What is 18 a a percentage of 144

Well, what is 18 as a fraction of 144?     That would be   18/144

NOW if you want to change a fraction to a percentage, you have to multiply it by 100 an add a percent sign :)

$${\frac{{\mathtt{18}}}{{\mathtt{144}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\frac{{\mathtt{25}}}{{\mathtt{2}}}} = {\mathtt{12.5}}$$

so that is 12.5%

$$\\4.9+15.21/1.9\\
\approx 5+15/2\\
\approx 5+7.5\\
\approx 12.5$$

exact answer

$${\mathtt{4.9}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{15.21}}}{{\mathtt{1.9}}}} = {\frac{{\mathtt{1\,226}}}{{\mathtt{95}}}} = {\mathtt{12.905\: \!263\: \!157\: \!894\: \!736\: \!8}}$$

Well the estimate is fairly close   :)