The axis of the parabola is parallel to Oy. The equation of the parabola is of the form: (x - x0)^2 = 4a(y - y0), where (x0, y0) is the vertex.
As we have 3 points through which the parabola passes, we can create 3 equations:
- (1,9)
(1 - x0)^2...
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The axis of the parabola is parallel to Oy. The equation of the parabola is of the form: (x - x0)^2 = 4a(y - y0), where (x0, y0) is the vertex.
As we have 3 points through which the parabola passes, we can create 3 equations:
- (1,9)
(1 - x0)^2 = 4a(9 - y0)...(1)
- (-2 , 9)
(-2 - x0)^2 = 4a(9 - y0)...(2)
- (21, 4)
(21 - x0)^2 = 4a(-4 - y0)...(3)
From (1) and (2)
(1 - x0)^2 = (-2 - x0)^2
=> 1 - x0 = x0 + 2
=> x0 = -1/2
Substituting in (3)
=>21.5^2 = 4a(-4 - y0) ...(4)
Substituting in (1)
=> 1.5^2 = 4a(9 - y0) ...(5)
Solving the equations (4) and (5) for a and y0, we get
4a = -460/13 and y0 = 16677/1840
The required equation of the parabola is (x + 1/2)^2 = (-460/13)(y - 16677/1840)