Question

Find the intersection. `y=sqrt(36-x^2)` and `y=8-x` ?

Answer 1

(5.4,2.6) and (2.6, 5.4)

Explanation:

If `y=sqrt(36-x^2)` and `y=8-x` then

`sqrt(36-x^2)=8-x`

Square both sides

`36-x^2=(8-x)^2`

Expand and collect like terms

`36-x^2=64-16x+x^2`

`2x^2-16x+28=0`

Divide by 2

`x^2-8x+14=0`

Use the formula

`x=[-(-8)\pmsqrt(8^2-(4xx1xx14))]/2`

`x=[8\pmsqrt(8)]/2`= `=[8\pm2sqrt2]/2`

`x=4+sqrt2` or `x=4-sqrt2`

`x=5.4142135624 or x =2.5857864376`

Substitute these into `y=8-x` to find the corresponding `y` values

`y= 8-5.4 => y =2.6`

and `y=8-2.6 =>y=5.4`