Question

Given the relation x = y 4 − 9 y 2, identify the x- and y- axis intercepts.

Answer 1

The x-intercepts are $(0,0)$

The y-intercepts are $(0,0),(0,3),(0,-3)$

Explanation:

The relation is $x=y^{4} -9y^{2}$

To find the x-intercept, let us substitute $y=0$ in the equation $x=y^{4} -9y^{2}$, we get,

$x=(0)^{4} -9(0)^{2} \\x=0$

Thus, the x-intercepts are $(0,0)$

To find the y-intercept, let us substitute $x=0$ in the equation $x=y^{4} -9y^{2}$, we get,

$0=y^{4}-9 y^{2}$

let us switch sides and solving, we get,

$\begin{aligned}y^{4}-9 y^{2} &=0 \\y^{2}\left(y^{2}-9\right) &=0 \\y^{2} &=0, y^{2}-9=0\end{aligned}$

Taking square root,

$y=0$ and $\begin{aligned}y^{2}-9 &=0 \\y^{2} &=9 \\y &=\pm 3\end{aligned}$

Thus, the y-intercepts are $(0,0),(0,3),(0,-3)$