Question

Can I get some help on these please

Answer 1

Ex 5

Simply multiply the equation by 6, in order to get rid of the denominators:

`(x)/(2)+(y)/(3) = 4 \iff 3x+2y=24`

Ex 6

We have to rearrange the equation in the form

`(x-x_0)^2+(y-y_0)^2=r^2`

So that
`r` is the radius, and
`2r` will be the diamater. We have to complete the squares: rewrite the equation as

`x^2-6x+y^2+8y=144`

You can see that
`x^2-6x` is the beginning of
`x^2-6x+9 = (x-3)^2`

Similarly,
`y^2+8y` is the beginning of
`y^2+8y+16 = (y+4)^2`

So, if we add 16 and 9 to both sides, the equation becomes

`x^2-6x+9+y^2+8y+16=144+9+16 \iff (x-3)^2+(y+4)^2=169`

So, now we know that
`r^2=169`, and thus the radius is 13, so the diameter is 26.