Find the equaion of the parabola

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The discussion centers on finding the equation of a parabola with its vertex at the origin and specified points. The user attempts to derive the equation for a parabola with a focus at (-4, -20), concluding that the equation is y² = -20x. However, other participants point out errors in the calculations, particularly regarding the focus and the value of 'a'. They emphasize the importance of verifying work and suggest that the provided point does not satisfy the derived equation. The conversation highlights the need for careful analysis in solving parabola equations.
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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)



my answer



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



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I sove only number one beacuse i am not sure from my answer

help me Are this solving corect or not ?
 
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r-soy said:
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)
These aren't very clear. I guess you mean the axis of symmetry (x-axis or y-axis) and a point on the parabola.
r-soy said:
my answer



A )

we have (-4, - 20 ) that mean the focus ( - 20 , 0 )
Why do you think the focus is at (-20, 0)?
r-soy said:
now we do comper 4ay = - 20

= -5
What equals -5?
r-soy said:
then the equation is : y2 = 4ax

= y2 =4(-5) x

=y2 = -20 x
y2 = 4ax is the right equation form, but you don't have the right value for a. The point (-4, -20) should make your equation a true statement, but (-20)2 \neq -20(-4).

You need to get into the habit of checking your work.
r-soy said:
----------------



I sove only number one beacuse i am not sure from my answer

help me Are this solving corect or not ?
 

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