Q. 4 H5.0( 5 Votes )

Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolas

y2 = 5x - 4y – 9

Answer :

Given equation of the parabola is y2 = 5x - 4y - 9



y2 + 4y = 5x - 9


y2 + 4y + 4 = 5x - 5


(y + 2)2 = 5(x - 1)


Comparing with the standard form of parabola (y - a)2 = 4b(x - c) we get,


4b = 5



The vertex is (c, a) = (1, - 2)


The focus is (b + c, a) =


The equation of the axis is y - a = 0 i.e, y + 2 = 0


The equation of the directrix is x - c = - b


Directrix is


Directrix is


Directrix is


Length of latus rectum is 4b = 5.


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