# How to find the x and y-intercepts of the following?

## $\left(i\right) 9 {x}^{2} = {y}^{2}$ $\left(i i\right) {y}^{2} - x y = 0$ Also plot their graphs.

Aug 29, 2017

Both have $0$ intercepts on $x$-axis and $y$-axis.

#### Explanation:

Remember to find $x$-intercept, put $y = 0$ and to find $y$-intercept, put $x = 0$.

(i) In $9 {x}^{2} = {y}^{2}$, if $y = 0$, we have $x = 0$ and if $x = 0$ we have $y = 0$ and hence intercepts on both the axes are $0$. Below is given the graph for the same. Note that it is equivalent to $\left(3 x + y\right) \left(3 x - y\right) = 0$ and hence represents two lines $3 x + y = 0$ and $3 x - y = 0$.

graph{9x^2=y^2 [-5, 5, -2.5, 2.5]}

(i) ${y}^{2} - x y = 0$, if $y = 0$, we have $x = 0$ and if $x = 0$ we have $y = 0$ and hence in this case too intercepts care $0$. Note that it is equivalent to $y \left(y - x\right) = 0$ and hence represents two lines $y = 0$ i.e. $x$-axis and $y = x$.

graph{y^2-xy=0 [-5, 5, -2.5, 2.5]}