Question

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Answer 1

Lines of symmetry are easily found: in 4x² + y² = 9, you can see that it doesn't matter if x is 2 or -2. Any value x gives the same result as -x, because of the square.
The same is true for y!

So:
If (a,b) is on the graph, then also (-a,b) is. So line of symmetry is ?
If (a,b) is on the graph, then also (a,-b) is. So line of symmetry is ?

Answer 2

The general equation for an ellipse with its center at the origin and x- and y-axes as lines of symmetry a is:\[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]
Suppose y=0, then, to satisfy the equation: \(x^2=a^2\), so \(x=\pm a\).
Also, if x=0, then \(y^2=b^2\), so \(y=\pm b\).

So the points (a, 0), (-a, 0), (0, b) and (-b, 0) are all on the graph.

Now look at your formula: \(4x^2 + y^2 = 9\). If you divide everyting by 9, you can convert this equation to the standard form. Then you know a and b, and you know what graph to choose!

Answer 3

Is it b?

Answer 4

If I convert the equation, I get \(\dfrac{x^2}{\left(\frac{3}{2}\right)^2}+\dfrac{y^2}{3^2}=1\). So (0,3) and (0,-3) are on the graph, and x- and y-axes are lines of symmetry.

Yes, must be B.