Focus at (0, -5), directrix y = 5
Solution
Let ( x 0 , y 0 ) be any point on the parabola. Find the distance between ( x 0 , y 0 ) and the focus. Then find the distance between ( x 0 , y 0 ) and directrix. Equate these two distance equations and the simplified equation in x 0 and y 0 is equation of the parabola.
The distance between ( x 0 , y 0 ) and (0, -5) is [(x 2 )+(y+5) 2 ]
The distance between ( x 0 , y 0 ) and the directrix, y = 5 is
| y 0 – 5|.
Equate the two distance expressions and square on both sides.
(x 0 2 )+(y 0 +5) 2 = ( y 0 – 5) 2
Simplify and bring all terms to one side:
Write the equation with y 0 on one side:
x 2 = -20y
This equation in ( x 0 , y 0 ) is true for all other values on the parabola and hence we can rewrite with ( x , y ).
So, the equation of the parabola with focus (0, -5) and directrix is y = 5 is
x 2 = -20y
.
Focus at (0- -5)- directrix y - 5SolutionLet ( x0 - y0 ) be any point.docx
1. Focus at (0, -5), directrix y = 5
Solution
Let ( x 0 , y 0 ) be any point on the parabola. Find the distance between ( x 0 , y 0 ) and the focus.
Then find the distance between ( x 0 , y 0 ) and directrix. Equate these two distance equations and
the simplified equation in x 0 and y 0 is equation of the parabola.
The distance between ( x 0 , y 0 ) and (0, -5) is [(x 2
)+(y+5) 2
]
The distance between ( x 0 , y 0 ) and the directrix, y = 5 is
| y 0 – 5|.
Equate the two distance expressions and square on both sides.
(x 0
2
)+(y 0 +5) 2
= ( y 0 – 5) 2
Simplify and bring all terms to one side:
Write the equation with y 0 on one side:
x 2
= -20y
This equation in ( x 0 , y 0 ) is true for all other values on the parabola and hence we can rewrite
with ( x , y ).
So, the equation of the parabola with focus (0, -5) and directrix is y = 5 is
x 2
= -20y
![Focus at (0, -5), directrix y = 5
Solution
Let ( x 0 , y 0 ) be any point on the parabola. Find the distance between ( x 0 , y 0 ) and the focus.
Then find the distance between ( x 0 , y 0 ) and directrix. Equate these two distance equations and
the simplified equation in x 0 and y 0 is equation of the parabola.
The distance between ( x 0 , y 0 ) and (0, -5) is [(x 2
)+(y+5) 2
]
The distance between ( x 0 , y 0 ) and the directrix, y = 5 is
| y 0 – 5|.
Equate the two distance expressions and square on both sides.
(x 0
2
)+(y 0 +5) 2
= ( y 0 – 5) 2
Simplify and bring all terms to one side:
Write the equation with y 0 on one side:
x 2
= -20y
This equation in ( x 0 , y 0 ) is true for all other values on the parabola and hence we can rewrite
with ( x , y ).
So, the equation of the parabola with focus (0, -5) and directrix is y = 5 is
x 2
= -20y](https://image.slidesharecdn.com/focusat0-5-directrixy-5solutionletx0-y0beanypoint-230201021749-03d4b553/85/Focus-at-0-5-directrix-y-5SolutionLet-x0-y0-be-any-point-docx-1-320.jpg)
