Question

evolute parabola x×2=4ay​

Answer 1

Answer:

The directrix of the parabola x2 = 4ay, having y-axis as its axis, passes through (0, -a), and has the equation y + a = 0. The focus of the parabola x2 = -4ay, having y-axis as its axis, passes through (0, a), and has the equation y - a = 0.

Step-by-step explanation:

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Answer 2

The directrix of the parabola x² = 4ay, having the y-axis as its axis, passes through (0, -a), and has the equation y + a = 0. The focus of the parabola x² = -4ay, having the y-axis as its axis, passes through (0, a), and has the equation y - a = 0.

For graph y² = 4ax

focus= (a, 0)

vertex = (0, 0)

semi-axis length = a

focal parameter= 2a

eccentricity = 1

directrix => x = -a

For graph y² = -4ax

focus = (-a, 0)

vertex = (0, 0)

semi-axis length = a

focal parameter = 2a

eccentricity = 1

directrix => x = a

For graph x² = -4ay

focus = (0, -a)

vertex = (0, 0)

semi-axis length = a

focal parameter = 2a

eccentricity = 1

directrix => y = a

For graph x² = 4ay

focus = (0, a)

vertex = (0, 0)

semi-axis length = a

focal parameter = 2a

eccentricity = 1

directrix => y = -a