find the focus and equation of parabola whose vertex is (6,-3) and diretrix is 3x - 5y + 1 = 0.

Equation of directrix=3x - 5y + 1 = 0--------(i)

Let the coordinate of focus = (a,b)

the axis of parabola is perpendicular to directrix.

So the equation of axis of parabola may be taken as x+y+k=0

it passes through (6,-3)

â‡’ 6-3+k=0

â‡’ k=-3

â‡’ the equation of axis of parabola is x+y-3=0---------------(ii)

Now, for the point of intersection of directrix and axis of parabola

On solving (i) and (ii), we get,

put the value of y in (i), we get,

Thus, the point of intersection of directrix and axis of parabola

Coordinates of

Vertex A (6,-3) is the mid-point of focus and

Coordinate of focus =

which is the equation of parabola

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