Use the locus definition of an ellipse to find the equation of the ellipse with focus (3,4), corresponding directrix line x+y=1 and 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=ae distance of directrix from center =a/e.
center is on the line y=x+1
half distance between focus and directrix =
from a/e, finding the length of a perpendicular from a point to a line.
i work it out to get
i work that out to be