If the vertex of a parabola is the point `(-3,0)` and the directrix is the line `x+5=0` , then find its equation.

Explanation

As , the co-ordinates of focus is the mid – point of the co-ordinates of vertex & the point of intersection of directrix and x or y axis respectively.

Focus`=(p, q)`

`-3=frac{p-5}{2}` and `0=frac{q+0}{2}`

`p-5=-6` and `q=0`

`p=-1` and `q=0`

Focus is`(-1, 0)`

For any point on parabola, `P(x,y)` the distance of focus from that point is always equal to the perpendicular distance from that point to the directrix. Perpendicular Distance (Between a point and line) = `frac{abs(ax_1+by_1+c)}{sqrt(a^2+b^2)}`, whereas the point is `(x_1, y_1)` and the line is expressed as `ax + by + c = 0 x + 5 = 0`

Using distance, `sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
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