Question

draw the parabola x^2= 4y​

Answer 1

Answer:

Find it , {MARK Me AS A BRILLIANT}

Step-by-step explanation:

Equation y2 = 4ax (a > 0) represents the equation of a parabola whose co-ordinate of the vertex is at (0, 0), the co-ordinates of the focus are (0, a), the equation of directrix is y = - a or y + a = 0, the equation of the axis is x = 0, the axis is along positive y-axis, the length of its latus rectum = 4a and the distance between its vertex and focus is a.

Standard form of Parabola x^2 = 4ay

Standard form of Parabola x^2 = 4ay

0Save

Solved example based on the standard form of parabola x2 = 4ay:

Find the axis, co-ordinates of vertex and focus, length of latus rectum and the equation of directrix of the parabola x2 = 6y.

Solution:

The given parabola x2 = 6y

⇒ x2 = 4 ∙ 32 y

Compare the above equation with standard form of parabola x2 = 4ay, we get, a = 32.

Therefore, the axis of the given parabola is along positive y-axis and its equation is x = 0.

The co-ordinates of its vertex are (0, 0) and the co-ordinates of its focus are (0, 3/2); the length of its latus rectum = 4a = 4 ∙ 32 = 6 units and the equation of its directrix is y = -a i.e., y = -32 i.e., y + 32 = 0 i.e., 2y + 3 = 0.