Find the equation of parabola :

vertex =(2,1)

directrix : x = y-1

Equation of directrix= x - y+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  (2,1)

⇒ 2+1+k=0

⇒ k=-3

 

⇒ 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 (2,1) is the mid-point of focus and 

 

Coordinate of focus =

 

 

which is the equation of parabola

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