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Give the focus, directrix, and axis for the parabola. x²=32y A. (0,8),y=-8,y-axis C. (8,0),x=8,x-axis

User Erenor Paz
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The given equation of the parabola is in the form x²=4ay. This is a standard equation for a parabola that opens upwards or downwards, directed along the y-axis.

The value of 'a' which is the distance from the vertex to the focus and the vertex to the directrix in a parabola, can be determined by dividing the coefficient on the right side of the equation, which is 32, by 4. This yields a = 8.

For a parabola in the form x²=4ay, the focus is at (0,a). Plugging in our value of 'a', we get that the focus of the parabola is at (0,8).

The directrix of a parabola in this form is the line y=-a. Substituting our value of 'a', we get that the directrix of the parabola is the line y=-8.

In this form, the parabola is symmetrical about the y-axis. Thus its axis is the y-axis.

In conclusion, based on the given parabolic equation, the focus is (0,8), the directrix is y=-8 and axis is the y-axis.

User Arjita Mitra
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