# Thread: Find the equaion of the parabola

1. ## Find the equaion of the parabola

Find the equaion of the parabola having its vertex at the origin , its axis as indicated :

A ) x-axis : (-4, - 20 )
b) y - axis : (30,-15 )
C) y - axis : (-root2,3)

A )
we have (-4, - 20 ) that mean the focus ( - 20 , 0 )
now we do comper 4ay = - 20
= -5

then the equation is : y2 = 4ax
= y2 =4(-5) x
=y2 = -20 x

----------------

I sove only number one beacuse i am not sure from my answer
help me Are this solving it corect ?

2. Originally Posted by r-soy
Find the equaion of the parabola having its vertex at the origin , its axis as indicated :

A ) x-axis : (-4, - 20 )
What does this mean? By "its axis" do you mean the axis of symmetry? If so does this mean that the axis of symmetry is the x axis? And what does the (-4, -20) mean?

b) y - axis : (30,-15 )
C) y - axis : (-root2,3)

A )
we have (-4, - 20 ) that mean the focus ( - 20 , 0 )
now we do comper 4ay = - 20
= -5

then the equation is : y2 = 4ax
= y2 =4(-5) x
=y2 = -20 x

----------------

I sove only number one beacuse i am not sure from my answer
help me Are this solving it corect ?

3. Originally Posted by HallsofIvy
What does this mean? By "its axis" do you mean the axis of symmetry? If so does this mean that the axis of symmetry is the x axis? And what does the (-4, -20) mean?
I thnik that mean ( x , y)
x = -4
y = -20

???

4. Originally Posted by r-soy
I thnik that mean ( x , y)
x = -4
y = -20

???
I understood that! My question was what does that particular point have to do with the parabola.

If the first problem is "Find the equation of the parabola having vertex at the orgin, axis of symmetry the x-axis, and containing the point (-4, -20) then:

Since the vertex is the origin and the axis of symmetry is the x-axis, the parabola must be of the form $\displaystyle y^2= ax$. Knowing that the point (-4, -20) is on that parabola means that x= -4, y= -20 must satisfy that equation: $\displaystyle (-20)^2= a(-4)$. Solve that for a.