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# use the distance formula to find the equation of a parabola with the g.docx

use the distance formula to find the equation of a parabola with the given focus and directrix

F(7,0), x = -7

Solution
P(x,y) lies on parabola iff distance of P from focus F(7,0) = distance of P from directrix x = -7
iff (x-7)^2+(y-0)^2 = (x+7)^2 (we are equating distance squares, distance from (x,y) to the line x = -7 is distance between (x,y) and (-7,y), since line perpendicular to x = -7 is parallel to x-axis, and thereby the foot of perpendicular from (x,y) to the line has y coordinate same)
iff y^2 = (x+7)^2-(x-7)^2
iff y^2 = 28x
.

use the distance formula to find the equation of a parabola with the given focus and directrix

F(7,0), x = -7

Solution
P(x,y) lies on parabola iff distance of P from focus F(7,0) = distance of P from directrix x = -7
iff (x-7)^2+(y-0)^2 = (x+7)^2 (we are equating distance squares, distance from (x,y) to the line x = -7 is distance between (x,y) and (-7,y), since line perpendicular to x = -7 is parallel to x-axis, and thereby the foot of perpendicular from (x,y) to the line has y coordinate same)
iff y^2 = (x+7)^2-(x-7)^2
iff y^2 = 28x
.

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