Question

System of conics help

Answer 1

Solutions are (6,3) and (-2,3).

Explanation:

From the first equation given we can write:

`(x-2)^(2) = 16-(y-3)^(2)\\`

substituting for
`(x-2)^(2)` in the second equation given we get

`(16-(y-3)^(2))/(16) + ((y-3)^(2))/(64) = 1`

`(-(y-3)^(2))/(16) + ((y-3)^(2))/(64) =0`

∴ y=3

Putting y=3 in the first equation we get

`(x-2)^(2) = 16`

x-2 = ±4

Hence x=6 or x=-2.