Sol. Given parabola is 9y 2 – 16x – 12y – 57 = 0 .....(1)

[Equation (1) is quadratic in y and linear in x, therefore bring all terms containing y on one side and then complete the square]

From (1), 9y 2 – 12y = 16x + 57

or .....(2)

This is of the form Y 2 = 4aX

where Y ≡ y – , X ≡ x + , 4a =

(i) Axis of parabola (1) is Y = 0 or y =

(ii) Co-ordinates of vertex are given by X = 0 and Y = 0 i.e. by x + = 0 and y – = 0

∴ Vertex is

(iii) Co-ordinates of focus are given by

X = a and Y = 0 i.e., by x + and y – = 0

∴ Focus is

(iv) Equation of the directrix is X = –a

or x + = ⇒ x =

(v) Length of latus rectum = |4a| =

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