An Equation of Parabola helps us to find attributes of parabola, after simplification of any given equation we can calculate vertex, focus, directrix etc of the parabola. Here is one such example.
Topic : Parabola
Parabola is a Geometrical figure with standard form x ² = -4ay
Question : Find the vertex, focus, diretrix, and axis of symmetry of the parabola y2+3x-2y-11=0
Solution :
y2+3x-2y-11=0
subtract 3x and add 11 on both the sides
y2+3x-2y-11=0
- 30 + 11 = - 30 + 11
-----------------------------
y2-2y = - 3x + 11
by completing the square method
y2-2y + 1 = - 3x + 11 + 1
(y - 1)2 = - 3x + 12
(y - 1)2 = - 3(x - 4)
Now x - 4 = 0 so x = 4
and y - 1 = 0 so y = 1
So vertex is (4,1)
Standard form is given by
(y - k)2 = 4p(x - h)
so here 4p = -3
p = - 3/4
Focus = (4 + (-3/4), 1) = (4 - 3/4 , 1) = (13/4, 1)
Directix x = 4 - (-3/4)
x = 4 + 3/4
x = 19/4
Axis of symmetry is
x = 4
Solving number of problems like this will help you to solve even difficult problems quickly, for more assistance contact calculus help or geometry help.
Topic : Parabola
Parabola is a Geometrical figure with standard form x ² = -4ay
Question : Find the vertex, focus, diretrix, and axis of symmetry of the parabola y2+3x-2y-11=0
Solution :
y2+3x-2y-11=0
subtract 3x and add 11 on both the sides
y2+3x-2y-11=0
- 30 + 11 = - 30 + 11
-----------------------------
y2-2y = - 3x + 11
by completing the square method
y2-2y + 1 = - 3x + 11 + 1
(y - 1)2 = - 3x + 12
(y - 1)2 = - 3(x - 4)
Now x - 4 = 0 so x = 4
and y - 1 = 0 so y = 1
So vertex is (4,1)
Standard form is given by
(y - k)2 = 4p(x - h)
so here 4p = -3
p = - 3/4
Focus = (4 + (-3/4), 1) = (4 - 3/4 , 1) = (13/4, 1)
Directix x = 4 - (-3/4)
x = 4 + 3/4
x = 19/4
Axis of symmetry is
x = 4
Solving number of problems like this will help you to solve even difficult problems quickly, for more assistance contact calculus help or geometry help.
