We know that the vertex is (0, 0) and the parabola is symmetric about the y-axis.
The equation of the parabola is either of the from x2 = 4ay or x2 = -4ay.
Given that the parabola passes through point (5, 2), which lies in the first quadrant.
So, the equation of the parabola is of the form x2 = 4ay, while point (5, 2) must satisfy the equation x2 = 4ay.
Then,
52 = 4a(2)
25 = 8a
a =\( \dfrac{25}{8}\)
Thus, the equation of the parabola is
x2 = 4 (\( \dfrac{25}{8}\))y
x2 = \( \dfrac{25y}{2}\)
2x2 = 25y
The equation of the parabola is 2x2 = 25y
Answered by Aaryan | 1 year agoAn equilateral triangle is inscribed in the parabola y2 = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
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