Sketch the graph

**Punch** · February 25th 2011, 03:54 AM

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

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

**Prove It** · February 25th 2011, 04:53 AM

It can't be done. Without knowing the value of $\displaystyle a$ you won't be able to sketch it.

**saravananbs** · February 25th 2011, 06:00 AM

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

yes, the value of a should be given.

if $a\in R$

then two figure are possible.
i)circle ( $a^2=4$ ) and
ii) ellipse ( $a^2 != 4$ ).
check it.

**Punch** · February 25th 2011, 11:35 PM

Originally Posted by Prove It

It can't be done. Without knowing the value of $\displaystyle a$ you won't be able to sketch it.

maybe providing the first part of the question may help,

sketch the graph A given by the equation $\frac{(x-3)^2}{4}-y^2=1$ and state the asymptotes, if any.

**HallsofIvy** · February 26th 2011, 02:23 AM

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 $\frac{(x-3)^2}{4}$ and $y^2$ 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 $\frac{(x-3)^2}{4}- y^2= 0$ .

Now, how about telling us what the problem really is?

**Punch** · February 26th 2011, 02:48 AM

Originally Posted by Punch

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

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

The real problem is Sketch the graph given by the equation $16x^2-64x+64+a^2y^2-16a^2=0$

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

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