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Answer:
see explanation
Step-by-step explanation:
The standard form of the equation of a parabola with it's principal axis along the x-axis and the vertex at the origin is
y² = 4ax ( a is the distance of the directrix/ focus from the vertex )
If 4a is positive the curve opens to the right. If 4a is negative the curve opens to the left.
y² = - 24x is in this form
Hence the vertex is at the origin and the curve opens to the left.
equating 4a = - 24 ⇒ a = - 6
Hence the focus is on the x-axis with coordinates (- 6, 0 )
The directrix is a vertical line 6 units to the right of the vertex with equation x = 6
The focus is at (- 6, 0 ), The directrix is given by x = 6.
What is the standard equation of a parabola?
The standard equation of a parabola is (y-k)²= -4p(x-h) ,for a parabola opening left.
Here (h,k) is the vertex of the parabola.
The equation of the parabola is y² = -24x
A parabola is a U shaped figure, whose all the points lie in one plane and are at a fixed distance form a point called as focus and the line called as directrix.
Here, the focus point is given by the coordinates ( h +p, k)
and the directrix is at x = h-p
For the equation y² = -24x,
On comparing to the standard equation,
The vertex is at the origin and the curve opens to the left.
On equating 4p = - 24
p = -6
The focus is at ( 0 +-6 , 0)
The focus is at (- 6, 0 )
The focus is on the x axis.
The directrix is given by
x = 0 - (-6)
x = 6
The directrix is a vertical line and 6 units to the right of the vertex.
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