Question

Fine the coordinates of points where `y=4x-8` intersects `(x-1)^2+(y-4)^2=25` ?

Answer 1

The points are `(4,8)` and `(30/17,-16/17)`

graph{(4x-8-y)((x-1)^2+(y-4)^2-25)=0 [-12.38, 12.93, -1.62, 11.04]}

Explanation:

Given:

`y=4x-8" [1]"`

`(x-1)^2+(y-4)^2=25" [2]"`

We can find the x coordinates of intersection by substituting equation [1] into equation [2]:

`(x-1)^2+(4x-8-4)^2=25`

`(x-1)^2+(4x-12)^2=25`

Expand the squares:

`17 x^2 - 98 x + 120 = 0`

Factor:

`(x-4)(17x-30)= 0`

`x = 4` and `x = 30/17`

Use equation [1] to find the corresponding y values:

`y = 4(4)-8`

`y = 8`

`y = 4(30/17)-8`

`y = -16/17`

The points are `(4,8)` and `(30/17,-16/17)`