Question

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1

Answer 1

for finding the equation , u have to first find distance between a point say (x,y) and focus(-5,5)

Answer 2

ie\[\sqrt{((x-(-5))^2+(y-5)^2}\]

Answer 3

after that u have to find distance between the point (x,y) and line y=-1

Answer 4

ie\[\left| y-(-1) \right|\]

Answer 5

now distance between the point (x,y) and the focus is equal to distance between (x,y) and the diretrix ...
hence the two equations will be equal

Answer 6

simplyfy the equation and get the desired equation of the parabola

Answer 7

if any problem u can ask?