Question

equation of the parabola when focus (3,4) and directrix is(x+y+7)​

Answer 1

let any point on the parabola be (x,y)

then

we know,in parabola,ratio,of distance from directrix to focus is 1:1 i.e their distance are equal

so,

{(x-3)^2+(y-4)^2}^1/2=(x+y+7)/(√2)

(x-3)^2+(y-4)^2=/(x+y+7)^2/2. (squaring on both side)

2x^2+18-12x+2y^2+32-16y=x^2+y^2+49+2xy+14y+14x

x^2+y^2-2x-30y+2xy+1=0