Find the equation of the parabola having focus (1, 1) and vertex at `(-3,-3)dot`

Explanation

Focus is at S(1,1) and vertex is at A (-3,-3).
So, equation of axis is x-y=0.

Let the directrix meet the axis at B.
Since A is midpoint of BC, coordinates of point B are (-7,-7).
Directrix is perpendicular to the axis and passes through the point B(-7,-7).
So, equation of directrix is x+y+14=0.
Now, equation of parabola is locus of point P(x,y) which is equidistant from focus and directrix.
`:." "sqrt((x-1)^(2)+(y-1)^(2))=(|x+y+14|)/(sqrt(2))`
`orx^(2)+y^(2)-2xy-32x-32y-192=0`, which is required equation of parabola.