In this page 'Equation of parabola 5' 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 (-2,-1) and the focus is (-4,-1).
Solution:
In the given focus and vertex, the y coordinates are same.So we can decide the given parabola is symmetric about x axis And the parabola is a vertical parabola whose y coordinate is squared.
Since the focus is above the vertex, the value of 'a' is positive and
that is the distance between the focus and vertex. Here the parabola opens left ward.
VF = a = √ (-4+2)² + (-1+1)²
a = √ (-2)² + (0)²
a = √ 4
a = 2
The equation of the parabola in the vertex form is
(y-k)² = - 4a(x-h)
(y+1)² = -4(2)(x+2)
y²+1+2y = -8x - 16
y²+ 8x + 2y 1+ 16 = 0
y²+ 8x + 2y + 17 = 0
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. | |
(6) Find the equation of the parabola whose vertex is the origin (0,0) and the focus is (0,4). |
Equation of parabola5 Equation of parabola5 Equation of parabola5 |
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:
It subtracts sadness and adds happiness in our life.
It divides sorrow and multiplies forgiveness and love.
Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?
Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”