# Equation of horizontal parabola passing through 3 points

find the equation of a parabola with axis parallel to x-axis and passing through (5,4), (11,-2), (21,-4).

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find the equation of a parabola with axis parallel to x-axis and passing through (5,4), (11,-2), (21,-4).

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## Re: analytic geometry

$y^2 + Dx + Ey + F = 0$

At (5, 4)

$16 + 5D + 4E + F = 0$

$5D + 4E + F = -16$ → equation (1)

At (11,-2)

$4 + 11D - 2E + F = 0$

$11D - 2E + F = -4$ → equation (2)

At (21,-4)

$16 + 21x - 4E + F = 0$

$21x - 4E + F = -16$ → equation (2)

From equations (1), (2), and (3), D = -2, E = -4, and F = 10

$y^2 - 2x - 4y + 10 = 0$

answer