91Ó°ÊÓ

We have given the following equation :-

$x^2+4y^2=16$.

We have to check the symmetry of this equation with respect to x-axis, y-axis and the origin.

The given equation is :-

$x^2+4y^2=16$.

We know that a graph is symmetrical about x-axis, if a point $\left(x,y\right)$lies on graph, then $\left(x,-y\right)$is also lies on graph.

So to check symmetry about x-axis, change $y$by $-y$in the given equation, then we have :-

localid="1646234197129" $$\begin{gathered} x^2+4{(-y)}^2=16 \\ ⇒x^2+4y^2=16 \end{gathered}$$.

The resulting equation is same as the given equation.

So we can say that the given equation is symmetric about x-axis.

The given equation is :-

$x^2+4y^2=16$.

We know that a graph is symmetrical about y-axis, if a point $\left(x,y\right)$lies on graph, then $\left(-x,y\right)$is also lies on graph.

So to check symmetry about y-axis, change $x$by $-x$in the given equation, then we have :-

$$\begin{gathered} {(-x)}^2+4y^2=16 \\ ⇒x^2+4y^2=16 \end{gathered}$$

The resulting equation is same as the given equation.

So we can say that the given equation is symmetric about y-axis.

The given equation is :-

$x^2+4y^2=16$.

We know that a graph is symmetrical about origin, if a point $\left(x,y\right)$lies on graph, then $\left(-x,-y\right)$is also lies on graph.

So to check symmetry about origin, change $x$by $-x$and $y$by $-y$in the given equation, then we have :-

$$\begin{gathered} {(-x)}^2+4{\left(-y\right)}^2=16 \\ ⇒x^2+4y^2=16 \end{gathered}$$

The resulting equation is same as the given equation.

So we can say that the given equation is symmetric about origin.