Use the locus definition of an ellipse to find the equation of the ellipse with focus (3,4), corresponding directrix linex+y=1and eccentricity 1/2.

so e=1/2, one focus(3,4)

let the center be (c,d)

then half the length of the major axis=a

distance of focus from center=aedistance of directrix from center =a/e.

center is on the liney=x+1

half distance between focus and directrix =

fromae,

froma/e, finding the length of a perpendicular from a point to a line.

so,

i work it out to get

also

i work that out to be

Thanks!