Every point on a conic is equidistant from the point (3,4) and the line defined by y = 2. Determine the equation of the locus.

Given

Focus is at (3,4)

Directrix is y = 2

Equation of parabola with focus at (a,b) and directrix at y= c is -

(x-a)^2 + (y-b)^2 = (y-c)^2..............................distance of any point from focus is equal to its distance from directrix

here,

(x-3)^2 + (y-4)^2 = (y-2)^2

y = (X^2 /4) -(3/2)*x + (21/4).........................final equation of given parabola

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