Answer:
y = 17/4
Explanation:
To determine the equation of the directrix of a parabola, we need to first identify the focus of the parabola. The general equation of a parabola is y = ax² + bx + c. Comparing this with the given equation y = 12x² - 6x + 10, we can say that a = 12, b = -6 and c = 10.
Now, to find the focus, we can use the formula, (h, k + (1/4a)) where h and k are the coordinates of the vertex. The vertex of this parabola can be determined by using the formula, h = -b/2a and k = c - b²/4a.
Substituting the values of a, b, and c in these formulas, we get;
h = -(-6)/2(12) = 1/4
k = 10 - (-6)²/4(12) = 9/2
So, the coordinates of the vertex are (1/4, 9/2).
Now, substituting these values in the formula, we get the focus as;
(h, k + (1/4a)) = (1/4, 9/2 + (1/4(12))) = (1/4, 23/4)
Hence, the focus of the parabola is (1/4, 23/4).
Now, the equation of the directrix of the parabola is y = k - (1/4a). Substituting the values of k and a in the formula, we get;
y = 9/2 - (1/4(12)) = 9/2 - 1/4 = 17/4
Therefore, the equation of the directrix is y = 17/4.
Hence, the equation of the directrix of the given parabola is y = 17/4.