Question

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

`(i) 9x^2=y^2`
`(ii) y^2-xy=0`

Also plot their graphs.

Answer 1

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 `9x^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 `(3x+y)(3x-y)=0` and hence represents two lines `3x+y=0` and `3x-y=0`.

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

(i) `y^2-xy=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(y-x)=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]}