+309 1. The general form of an parabola is 3x^2 + 24x − 2y + 52 = 0 .
What is the standard form of the parabola?
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2.The directrix of a parabola is x = 4. Its focus is (2,6) .
What is the standard form of the parabola?
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+37157 Here is ONE standard form
3x^2+24x-2y+52 = 0 divide by 3
x^2 + 8x -2/3 y + 52/3 complet 'x' square
(x+4)^2 = 16 +2/3 y -52/3
(x+4)^2 = 2/3 y -4/3
(x+4)^2 = 2/3 (y - 2)
+130071 3x^2 + 24x - 2y + 52 = 0 rearrange as
2y = 3x^2 + 24x + 52 divide both sides by 2
y = (3/2)x^2 + 12x + 26 factor out the (3/2)
y = (3/2) [ x^2 + 8x + 52/3 ]
Complete the square on x........take 1/2 of 8 = 4 ......square it = 16.....add and subtract within the parentheses
y = (3/2) [ x^2 + 8x + 16 + 52/3 - 16 ]
Factor the first three terms in the parentheses and simplify the last two terms
y = (3/2) [ (x + 4)^2 + 4/3 ]
Distribute the (3/2) over the terms in the parentheses
y = (3/2) (x + 4)^2 + 2 or
(y - 2) = (3/2) (x + 4)^2
+130071 Second one
The vertex will be at ([4 + 2] / 2, 6 ) = ( 3, 6) = (h, k)
This parabola opens to the left because the directrix is to the right of the focus
The form is
-4a ( x - h) = (y - k)^2
a = the distance between the vertex and focus = 1
So we have that
-4 (1) (x - 3) = (y - 6)^2
-4 (x - 3) = (y - 6)^2
Here's the graph : https://www.desmos.com/calculator/9wy9pmdttx
