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`        find the equation of parabola , when the vertex is(2,1) and directrix is x=y-1`
2 years ago

```							Dear student 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 parabolaOn solving (i) and (ii), we get, y = 2put the value of y in (i), we get, x = 1 Thus, the point of intersection of directrix and axis of parabola (X, Y) = (1, 2)Coordinates of z = (1,2) Vertex A (2,1) is the mid-point of focus and z = (1,2)2 = (a+1)/2a = 3 1 = (b+2)/2b = 0 Coordinate of focus = (3,0)  Now you can simply get the equation of parabola byPS = PM
```
2 years ago
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