SOLUTION: Please help me solve this equation Find the Parabola properties and graph y^2+6x+6y=39 Vertex: Focus: Directrix: Axis of symmetry: Endpoints of latus retum:

Question 1044782: Please help me solve this equation
Find the Parabola properties and graph
y^2+6x+6y=39

Vertex:
Focus:
Directrix:
Axis of symmetry:
Endpoints of latus retum:

Found 2 solutions by MathLover1, solver91311:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Find the Parabola properties and graph
given:

Vertex:
first write your equation in vertex form (since y squared) where and are and coordinates of the vertex

and
vertex is at ( , )
Since the value of a is negative, the parabola opens left.
Focus:
The focus of a parabola can be found by adding p to the x-coordinate h if the parabola opens left or right.
(,)
Find p, the distance from the vertex to the focus.
Find , the distance from the vertex to a focus of the parabola by using the following formula.

since , we have

(,)
(,)
( , )->focus
Directrix:
The directrix of a parabola is the vertical line found by subtracting p from the x-coordinate h
of the vertex if the parabola opens left or right.

Axis of symmetry:
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
vertex is at ( , )
( , )->focus
and that will be
Endpoints of latus retum:
length of latus rectum =
endpoints of the latus rectum: (,) and (,)
since , and we have
(,) and (,)
(,) and (,)
(,) and (,)

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

Since is the squared variable, your parabola is "sideways" and the general equation is:

The vertex is at the point and the directed distances from the vertex to the focus and the directrix are and .

The axis of symmetry is the horizontal line through the vertex, so

The focus is and the directrix is the vertical line

The latus rectum is the segment with endpoints and .

Now the trick is to get into the form

Now complete the square in the LHS:

Factor both sides:

Solve for

So, by inspection you have:

, , and .

You can do the rest of the arithmetic.

John

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

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