The equation of the directrix of the parabola y = -⁵/₈x²- 3x + 4 is; y = 8
How to find the equation of the directrix?
We are given the equation of the parabola as;
y = -⁵/₈x²- 3x + 4
multiply through by 8 to get;
8y = -5x² - 24x + 32
8y - 32 = -5x² - 24x
This can be simplified further to get;
8y - 32 = -5(x² + 4.8x)
Using method of completing the square, we have;
(x + 2.4)² = -(1.6)(y - 7.6)
This is a vertical parabola that opens down.
The standard form of a parabola is;
(x - h)² = 4p(y - k)
Thus, the vertex is at the point (h, k) which will be (-2.4, 7.6)
4p = -1.6
p = -1.6/4
p = -0.4
The directrix will be;
y = k - p
y = 7.6 - (-0.40)
y = 7.6 + 0.40
y = 8
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