How do I properly do questions like these? I simply each equation by inputting the value into the variable but after that I am confused as to what I am supposed to do after?
Asked
Active
Viewed 182 times
1

2When you put in, for example, $x=0$ then you have $5y^{2}+z^{2}=4$. Is this an equation of a circle? An ellipse? What are the coordinates where it intercepts the other axes? – Morgan Rodgers Jan 12 '20 at 00:45

Where is it from? Could you give us the source of the problem? – Alain Remillard Jan 12 '20 at 01:43

It is the equation of an ellipse but I am unsure of how to apply it. – OGK Jan 12 '20 at 23:29
1 Answers
0
After you replace the variable, you look at the curve in the plane that you get. For instance, in the first case you put $z=1.5$, and you get $$ 2x^2+5y^2+2.25=4, $$ or $$ 2x^2+5y^2=1.75. $$ We may rewrite this as $$ \frac{x^2}{\left(\frac{\sqrt{1.75}}{\sqrt2}\right)^2}+\frac{y^2}{\left(\frac{\sqrt{1.75}}{\sqrt5}\right)^2}=1, $$ where we see that get an ellipse centered at the origin crossing the $x$axis at $\pm\frac{\sqrt{1.75}}{\sqrt2}\simeq\pm0.94$ and the $y$axis at $\pm\frac{\sqrt{1.75}}{\sqrt5}\simeq\pm0.6$, which seems to be D in your options.
Martin Argerami
 179,760
 14
 120
 240


You mean this? $$\frac{x^2}{\left(\frac{\sqrt{1.75}}{\sqrt2}\right)^2}=\frac{2x^2}{1.75}.$$ – Martin Argerami Jan 12 '20 at 23:32

Yes, how did you go from 2x^2+5y^2 = 1.75 to the the rewritten equation at the end. did you set x or y to 0 then solve for each variable independently? – OGK Jan 12 '20 at 23:34

Still not sure if you are talking about the equation of the ellipse, or its intercepts. – Martin Argerami Jan 12 '20 at 23:39

Both of them. For the interepts did you just set one of the variable equal to 0 and then just solve for it and for the equation how did you get that answer? – OGK Jan 12 '20 at 23:41

Yes. If $y=0$, then the equation becomes $$\frac{x^2}{\left(\frac{\sqrt{1.75}}{\sqrt2}\right)^2}=1,$$ so $${x^2}={\left(\frac{\sqrt{1.75}}{\sqrt2}\right)^2}.$$ – Martin Argerami Jan 12 '20 at 23:43

Thank you one last question if we are plotting the zintercept would that just go on the regular yaxis?, what I mean by this is in the equation 2x^2 + z^2 = 1.1875 we have a clear x and z intercept. So would the x intercept go on the x axis and the z go on the yaxis? – OGK Jan 12 '20 at 23:47

You can name the variables any way you want. When you are doing $x$ and $z$, you need to display things in the $xz$plane. Drawing it in perspective at an angle will give you nothing, though, so you just draw it as a plane. – Martin Argerami Jan 12 '20 at 23:50