what is an equation of a parobola with the given vertex and focus?
vertex(5,4) and focus(8,4)
Can someone show me the steps to get the equation please?
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100% Parabolas Unit 7 Lesson 2
1.) focus: (0,3) ; directrix: y = -3
2.) x=-1/19^y^2
3.) y=1/8x^2
4.) vertex (3,3); focus (3,6); directrix y= 0
5.) 1/12 (y-4)^2+5
So x=1/12(y-4)^2+5 would be the answer?
Countess Nightmare and Imposter are 100% correct! Thankssss!
the parabola with vertex (0,0) and focus (p,0) is
4px = y^2
We need to shift the vertex to (5,4), so substitute
4p(x-5) = (y-4)^2
The focus is 3 units away from the vertex, so p=3, and we have
12(x-5) = (y-4)^2
Correct ^
To find the equation of a parabola given the vertex and focus, follow these steps:
Step 1: Identify the vertex coordinates. In this case, the vertex is (5, 4).
Step 2: Identify the focus coordinates. In this case, the focus is (8, 4).
Step 3: Determine if the parabola opens horizontally or vertically. Since the y-coordinates of both the vertex and focus are the same, the parabola opens horizontally.
Step 4: Use the formula for the standard equation of a horizontal parabola, which is [(y - k)^2] = 4p(x - h), where (h, k) represents the vertex coordinates and p represents the distance from the focus to the vertex.
Step 5: Calculate the value of p, which is the distance from the vertex to the focus. In this case, p = 8 - 5 = 3.
Step 6: Substitute the values of h, k, and p into the equation. The equation becomes [(y - 4)^2] = 4(3)(x - 5).
Step 7: Simplify the equation. [(y - 4)^2] = 12(x - 5).
Therefore, the equation of the parabola with the given vertex and focus is [(y - 4)^2] = 12(x - 5).