SOLUTION: (y + 5/2)2 = -5(x - 2/9) please help me know What is the vertex, focus, directrix and axis of symmetry of this equation of a PARABOLA?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: (y + 5/2)2 = -5(x - 2/9) please help me know What is the vertex, focus, directrix and axis of symmetry of this equation of a PARABOLA?       Log On


   

Question 1059943: (y + 5/2)2 = -5(x - 2/9)
please help me know What is the vertex, focus, directrix and axis of symmetry of this equation of a PARABOLA?
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You mean, like this: %28y+%2B+5%2F2%29%5E2+=+-5%28x+-+2%2F9%29

This parabola has horizontal symmetry axis and opens to the left, and vertex is the point farthest to the right.

These should help you enough for understanding how to answer the questions:

Deriving equation for parabola if given focus and directrix - for vertex AT the origin

Differently oriented, and vertex is not at Origin

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


For the general parabola with a horizontal axis of symmetry:



The vertex is at , the focus is at , the directrix is the vertical line that passes through , namely , and the axis of symmetry is the horizontal line that passes through both the vertex and the focus, namely .

For your parabola, the vertex is at and , so

You can do the rest of the arithmetic. Be careful with your signs. The focus on this one is correctly placed if it is to the left of the vertex, i.e. your parabola opens to the left.

John

My calculator said it, I believe it, that settles it