Question

How to find the coordinates?

Answer 1

`(x, y)=(4/9, 2)`

Explanation:

`4y=9x+4`
`y^2=9x`
All we need to do is to solve the system of equations, the solutions are the required points, so:
`9x=4y-4`
`x=(4y-4)/9`
`y^2=9*(4y-4)/9`
`y^2-4y+4=0`
`(y-2)^2=0`
`y=2`
`x=4/9`
thus the required coordinated are:
`(x, y)=(4/9, 2)`

Answer 2

`(x,y)to(4/9,2)`

Explanation:

`4y=9x+4to(1)`

`y^2=9xto(2)`

`"from equation "(1)color(white)(x)9x=4y-4to(3)`

`"substitute "9x=4y-4" in equation "(2)`

`y^2=4y-4larrcolor(blue)"rearrange and equate to zero"`

`rArry^2-4y+4=0`

`rArr(y-2)^2=0rArry=2`

`"substitute "y=2" in equation "(3)`

`9x=8-4rArrx=4/9`

`"point of contact "=(4/9,2)`
graph{(y-9/4x-1)(y^2-9x)=0 [-10, 10, -5, 5]}