## anonymous 4 years ago x^2+y^2=20 y=x^2 A. {(4, -2), (4, 2) B. {(-2, 4), (2, 4) C.(2, 4) D.(3, 9)

1. anonymous

X^2+Y^2=20

2. anonymous

Y=X^2

3. anonymous

i think for this one easiest to check answer and see which ones work

4. anonymous

i DONT KNOW HOW TO DO IT

5. anonymous

$$x^2+y^2=20$$ and $$y=x^2$$ $$\implies x^4+x^2=20$$

6. perl

y^2 + y - 20 = 0 after substitution , (y+5)(y-4) = 0

7. anonymous

$(-2+x) (2+x) \left(5+x^2\right) =0$

8. anonymous

y + y^2 = 20 y^2 + y + 1/4= 20 +1/4 (y+1/2)^2 = 81/4 y + 1/2 = 9/2 y = 4 knowing that... 4 = x^2 x = +/- 2 so it's {(-2,4)(2,4)

9. anonymous

for example, try (2,4) $2^2=4$ so second equation is satisfied, but $2^2+4^2=4+16=20$ so first equation is satisfied as well

10. anonymous

Yes substitution is the best choice here.

11. anonymous

now try $(-2)^2=4$ true and $(-2)^2+4^2=20$ also true

12. perl

{ (sqrt 5, 5) ( -sqrt 5 , 5 ) ( 2, 4) (-2, 4) }

13. anonymous

Analytically it would be messy.

14. anonymous

(3,9) does not work because although $3^2=9$ is true $3^2+9^2\neq 20$ so that one is out

15. perl

the 5's dont work, scratch that

16. anonymous

and (4,-2) does not work because $4^2\neq -2$