Sketch the graph given by the equation $\displaystyle 16x^2-64x+64+a^2y^2-16a^2=0$

I'm not sure how to present the equation to a form suitable for graph sketching(eg. hyperbola, ellipse, circle)

Printable View

- Feb 25th 2011, 03:54 AMPunchSketch the graph
Sketch the graph given by the equation $\displaystyle 16x^2-64x+64+a^2y^2-16a^2=0$

I'm not sure how to present the equation to a form suitable for graph sketching(eg. hyperbola, ellipse, circle) - Feb 25th 2011, 04:53 AMProve It
It can't be done. Without knowing the value of $\displaystyle \displaystyle a$ you won't be able to sketch it.

- Feb 25th 2011, 06:00 AMsaravananbsQuote:

Sketch the graph given by the equation $\displaystyle 16x^2+a^2y^2-64x+64-16a^2=0$

if $\displaystyle a\in R$

then two figure are possible.

i)circle ($\displaystyle a^2=4$) and

ii) ellipse ($\displaystyle a^2 != 4$).

check it. - Feb 25th 2011, 11:35 PMPunch
- Feb 26th 2011, 02:23 AMHallsofIvy
I don't see how that has anything to do with the question you first posted! However, here is a good way to find asymptotes for a hyperbola (which that clearly is). If x and y are both very, very large numbers then so are $\displaystyle \frac{(x-3)^2}{4}$ and $\displaystyle y^2$ so that, in comparison, we can ignore "1". That is, for very, very large x and y, the graph is almost identical with the two straight lines given by $\displaystyle \frac{(x-3)^2}{4}- y^2= 0$.

Now, how about telling us what the problem**really**is? - Feb 26th 2011, 02:48 AMPunch
The real problem is Sketch the graph given by the equation $\displaystyle 16x^2-64x+64+a^2y^2-16a^2=0$

and the difficulty i am facing is expressing the equation in a form suitable for sketching like a hyperbola, ellipse or circle equation

and i am also allowed to state the intercepts in terms of a too