Equation of parabola6

In this page 'Equation of parabola 6' we are going to find the equation of the parabola for the given information.

Question 6:

Find the equation of the parabola whose vertex is the origin (0,0) and the focus is (0,4).

Solution:

In the given focus and vertex, the x coordinates are same. So the focus and vertex are in the same axis x=0 .And the parabola is a vertical parabola whose x coordinate is squared.

Since the focus is above the vertex, the value of 'a' is positive and that is the distance between the y coordinates. Here the parabola opens up.

a = 4 - 0 = 4.

The equation of the parabola in the vertex form is

(x-h)² = 4a(y-k)

(x-0)² = 4(4)(y-0)

x² =  16y

In the previous pages we found the equation of the parabola in two methods, as directrix is given. Here in this problem since the directrix is not given we found the equation of the parabola using only equation method (that is, using equation of parabola in the vertex form).

Students can follow the above method to derive the equation of the parabola. Parents and teachers can guide the students to understand the method of 'Equation of parabola 6' and guide them to do the practice problems using the same method.

 Practice Questions Solution (1) Find the equation of the parabola whose focus is (3,0) and the equation of the directrix is x=-3. (2) Find the equation of the parabola whose focus is (4,1) and the equation of the directrix is x = 0. (3) Find the equation of the parabola whose vertex is the origin (0,0) and the equation of the directrix is x = 2. (4) Find the equation of the parabola whose vertex is (1,2) and the equation of the directrix is y = 0. (5) Find the equation of the parabola whose vertex is (-2,-1) and the focus is (-4,-1). (6) Find the equation of the parabola whose vertex is the origin (0,0) and the focus is (0,4). Equation of parabola6  Equation of parabola6 Equation of parabola6

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