Question

Question #d8af6

Answer 1

we are to find the vertex and axis of the parabola whose focus (F) is (3,4) and directrix is `3x+4y+25=0........[1]`.

We know that axis of a parabola is the straight line perpendicular to its directrix passing through focus,

Any straight line perpendicular to directrix `3x+4y+25=0` is `4x-3y+c=0`

As it passes through we can write

`4xx3-3xx4+c=0=>c=0`

So equation of the axis is `4x-3y=0.....[2]`

Solving [1] and [2] we get `x=-3 and y =-4`

So the coordinates of point (A) of intersection of directrix and axis is `(-3,-4)`

Now let the coordinates of Vertex (V) be `(h,k)`

V is the mid point of AS ,

So `h=(-3+3)/2=0 and k=(-4+4)/2=0`

Hence the coordinates of vertex (V) is `(0,0)`