## Equation of parabola1

In this page 'Equation of parabola 1' we are going to find the equation of the parabola for the given information.

Question 1:

Find the equation of the parabola whose focus is (3,0) and the equation of the directrix is x=-3.

Solution:

Method I

Here the S is the given focus (3,0) and the directrix is x=-3.

Let P(x,y) be a point on the parabola.

If we draw a line PM perpendicular to the directrix, we know that

SP/PM = 1. (as it is a parabola, SP/PM=e=1)

SP²    =  PM²

(x-3)²+(y-0)² = [(x+3)/√(1²+0²)}]²

x²+9-6x+y²    =  (x+3)²/1

x²-6x+9+y²    =   x²+6x+9

Simplifying we get

y²     = 12x               Equation of parabola1 Equation of parabola1

Method II:

We know that vertex is half way between the focus and directrix. We also know that the parabola curves away from the directrix. The vertex is the origin(0,0). Since the parabola opens in the right hand side 'a' must be positive and the value of a is the distance between the focus and vertex and the distance between the vertex and directrix. So here the value of a is 3

So the equation of the parabola in the vertex form is

(y-k)² = 4a(x-h)

(y-0)² = 4(3)(x-0)

y²     = 12x

Students can follow either method to derive the equation of the parabola. Parents and teachers can guide the students to understand both methods of 'Equation of parabola 1' and guide them to do the practice problems using one of the above methods.

 Practice Questions Solution (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).

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: