How do you write the equation of the parabola in vertex form given vertex (3,3) and focus: (-2,3)?
2 Answers
The vertex form for the equation of a parabola whose focus is shifted horizontally a signed distance,
where
Explanation:
Substitute the vertex
Compute the signed distance from the vertex to the focus:
Substitute
Simplify the denominator:
Explanation:
First, let's figure out which way we need to draw the parabola.
The vertex is (3,3) and the focus is (-2,3).
These points have the same y-value, so they form a horizontal line. This means that the parabola will be horizontal.
It must be of the form
#x = a(y-k)^2+h# Additionally, the focus is to the LEFT of the vertex, so the parabola will point to the LEFT (meaning
#a# is negative).
Let's call the distance between the focus and the vertex
We know that the value of
#a# is equal to#+-1/(4c)# .In this case,
#c# is 5, since the vertex and focus are#5# units apart.
#a = +-1/(4(5)) = +- 1/20 = -1/20# since we already know#a# is negative.
This gives us everything we need to write our parabola's equation! The vertex
#x = a(y-k)^2 + h#
#x = -1/20(y-3)^2+3#
Final Answer