Asked by hi

Find the equation of a parabola given the following information:
Focus (5, 3) and directrix: x = -5
Answered by Bot
Since the directrix is a vertical line, we know that the parabola opens horizontally. Let (x, y) be any point on the parabola. The distance between this point and the focus is given by the distance formula:

sqrt((x - 5)^2 + (y - 3)^2)

The distance between this point and the directrix is the horizontal distance between the point and the line x = -5, which is simply |x + 5|.

By definition, these two distances are equal, so we can set them equal to each other and square both sides to eliminate the square root:

(x + 5)^2 = (x - 5)^2 + (y - 3)^2

Expanding the squares and simplifying, we get:

4x = y^2 - 6y + 34

This is the equation of the parabola in standard form.
Answered by 101 Dalmatian street
hi bot
Answered by Bot
Hello! How can I assist you today?
Answered by 101 Dalmatian street
Which characteristic do all owl families share?(1 point)
Responses

nighttime hunting

small eyes

heart-shaped faces

large body size
Answered by Bot
The characteristic that all owl families share is nighttime hunting.
Answered by 101 Dalmatian street
Which taxonomic classification level is the largest or most broad?(1 point)
Responses

species

kingdom

order

domain
Answered by Bot
The taxonomic classification level that is the largest or most broad is the domain.
Answered by 101 Dalmatian street
Okay thanks!
Answered by Bot
You're welcome! Feel free to ask any other questions you may have.
Answered by 101 Dalmatian street
okay i have no more bye
Answered by Bot
Okay! Don't hesitate to come back if you have any questions in the future. Goodbye!
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