## anonymous one year ago Using a directrix of y = -2 and a focus of (2, 6), what quadratic function is created?

1. AlexandervonHumboldt2

Focus: (2, 6) Any point, (x0 , y0) on the parabola satisfies the definition of parabola, so there are two distances to calculate: Distance between the point on the parabola to the focus Distance between the point on the parabola to the directrix $\sqrt{(x_0-a)^2+(y_0-b)^2}$ $\sqrt{(x_0-2)^2+(y_0-0)^2}$ y=-2 dirextix Distance between point ( x0 , y0) and the line y=-2 |y_0+2| Equate the two expressions. $\sqrt{(x_0-2)^2+(y_0-0)^2}=\left| y_0+2 \right|$ now solve this:

2. AlexandervonHumboldt2

square both sides: $(x_0-2)^2+y_0^2=(y_0+2)^2$

3. AlexandervonHumboldt2

simplify: $x^2-2x+4+y^2=y^2+2y+4$

4. AlexandervonHumboldt2

simplify: $x^2-2x+4-4+y^2-y^2=2y$

5. AlexandervonHumboldt2

$x^2-2x=2y$

6. AlexandervonHumboldt2

$y=\frac{ x^2-2x }{ 2 }$

7. AlexandervonHumboldt2

i might have done a mistake though haven't made such question for long time

8. anonymous

thats not any of my choices :/

9. AlexandervonHumboldt2

10. anonymous

$f(x)= -\frac{ 1 }{ 8 } (x-2)^{2}-2$

11. anonymous

$f(x)=\frac{ 1 }{ 16 } (x-2)^{2}-2$

12. anonymous

and then the same as the first except positive 1/8 and same as the second but negative 1/16

13. AlexandervonHumboldt2

OHHHHHHHHHHHHH i counted with focus (2, 0) not (2, 6) wait lemme redo it

14. anonymous

okey

15. AlexandervonHumboldt2

$\sqrt{(x_0-2)^2+(y_0-6)^2}=\left| y_0+2 \right|$

16. AlexandervonHumboldt2

$(x_0-2)^2+(y_0-6)^2=(y_0+2)^2$

17. AlexandervonHumboldt2

$(x-2)^2+y^2-12y+36=y^2+2y+4$

18. AlexandervonHumboldt2

$(x-2)^2+32=14y$

19. AlexandervonHumboldt2

woops mistake again

20. AlexandervonHumboldt2

(x-2)^2+y^2-12y+36=y^2+4y+4

21. AlexandervonHumboldt2

(x-2)^2+32=16y y=1/16*(x-2)^2+2 i the answer if i again didn't made a mistake somewhere

22. anonymous

thanks! ill let you know in 1 sec

23. anonymous

yep! it was right!! i got 100/100 on my quiz thanks!

24. AlexandervonHumboldt2

np sorry for taking so much time

25. AlexandervonHumboldt2

np sorry for taking so much time