## cutiecomittee123 one year ago How do I find the coordinates of the vertex of a parabola? Also How do I find the Foci?

1. CoconutJJ

Complete The Square Method.

2. anonymous

the vertex is the highest or the lowest point of a parabola in the form $$f(x) = a(x-h) + k$$ (h, k) is the vertex on condition that a is not equal to zero

3. Loser66

What is the parabola form? particular problem, please

4. cutiecomittee123

OMG wow I meant to say hyperbola

5. CoconutJJ

well that's a different story...

6. cutiecomittee123

and the equation given is x^2/16 - y^2/25 =1

7. CoconutJJ

I don't think there is a vertex...

8. cutiecomittee123

well there are vertices

9. cutiecomittee123

because with a hyperbola there are basically two parabolas

10. CoconutJJ

dy/dx*

11. Loser66

YOur hyperbola has the form $$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$$ where $$a^2 = 16$$ and $$b^2 = 25$$

12. Loser66

hence, its graph is |dw:1432872366397:dw|

13. Loser66

Foci will lie on x-axis, and it is calculated by $$c^2 = a^2+b^2 = 16+25 =41$$ hence, foci are $$(\pm \sqrt {41},0)$$

14. Loser66

One more thing: it doesn't have directrix but the center, and you know how to find the center, right? just (0,0)

15. cutiecomittee123

Wait no, how is the center found??

16. Loser66

half way of foci, in this case, it is ALWAYS =(0,0)|dw:1432873065615:dw|

17. cutiecomittee123

how do i find the vertices? @Loser66

18. Loser66

what??? the vertices is a on your expression

19. anonymous

can you help me with some math

20. anonymous