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Find the Equation of the Parabola that Satisfies the Following Conditions: Focus (0, –3); Directrix Y = 3 - CBSE (Arts) Class 11 - Mathematics

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Question

Find the equation of the parabola that satisfies the following conditions: Focus (0, –3); directrix y = 3

Solution

Focus = (0, –3); directrix y = 3

Since the focus lies on the y-axis, the y-axis is the axis of the parabola.

Therefore, the equation of the parabola is either of the form x2 = 4ay or

x= – 4ay.

It is also seen that the directrix, y = 3 is above the x-axis, while the focus

(0, –3) is below the x-axis. Hence, the parabola is of the form x2 = –4ay.

Here, a = 3

Thus, the equation of the parabola is x2 = –12y.

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Solution Find the Equation of the Parabola that Satisfies the Following Conditions: Focus (0, –3); Directrix Y = 3 Concept: Parabola - Standard Equations of Parabola.
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