Find the equation of the parabola that satisfies the following conditions: Focus (6, 0); directrix x = –6

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asked Feb 9, 2018 in Mathematics by Rohit Singh (61,782 points) 35 133 356
Find the equation of the parabola that satisfies the following conditions: Focus (6, 0); directrix x = –6

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answered Feb 9, 2018 by sameer (82,980 points) 5 11 37

Focus (6, 0); directrix, x = –6
Since the focus lies on the x-axis, the x-axis is the axis of the parabola.
Therefore, the equation of the parabola is either of the form y2 = 4ax or
y2 = – 4ax.
It is also seen that the directrix, x = –6 is to the left of the y-axis, while the focus (6, 0) is to the right of the y-axis.
Hence, the parabola is of the form y2 = 4ax.
Here, a = 6
Thus, the equation of the parabola is y2 = 24x.

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