Question

Which is the equation of the parabola that opens to the right, has a focus at (3, 0), and has a directrix at x = –3?

Answer 1

help please

Answer 2

A parabola is a locus of all points that are equidistant from a fixed point(ie focus) and a fixed line(ie directrix)
Take any point (x,y)
The distance of this point from the focus should be equal its distance from the directrix.
The distance between this point and the focus is:
\[\sqrt{(x-3)^{2}+(y-0)^{2}}\]
The perpendicular distance of this point from the directrix is:
\[\left| x+3/\sqrt{3^{2}+0^{2}} \right|\](This is the formula of perpendicular distance of a point from a line).
Now, equate these two, square each side(squaring removes the modulus operator) and find the equation in terms of x and y
Did you understand?