Question

MEDAL AND FAN!!!!!
What is the equation of a parabola with vertex at (1, −3) and focus at (−2, −3)?

Answer 1

I am aware of the formula of parabola and how to find the focus,directrix etc.

Answer 2

@mathmale

Answer 3

@mathmate

Answer 4

Pls help

Answer 5

@ganeshie8

Answer 6

If you know how to find the focus, directrix, etc, do you visualize the parabola as shown above?

Answer 7

yes

Answer 8

Since the vertex and focus both lie on a horizontal line, the axis of the parabola is horizontal. ok so far?

Answer 9

Can you give me the equation of the directrix?

Answer 10

i think it is y=-5

Answer 11

Not really!
The directrix is perpendicular to the axis of the parabola, so it is a vertical line, something like x=... .
Also, the directrix and focus are on opposite sides of the vertex, so in this case, the directrix is a vertical line to the RIGHT of the vertex.
Making sense so far?

Answer 12

x=5 ?correct?

Answer 13

Almost.
The distance of the directrix to the vertex is the same as that between the focus and vertex.
Can you give it another try?

Answer 14

x=4

Answer 15

Great! It's because 4-1=1-(-2), right?
Can you draw the directrix on the directrix?

Answer 16

yes