Q. 4 H5.0( 5 Votes )

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

y^{2} = 5x - 4y – 9

Answer :

Given equation of the parabola is y^{2} = 5x - 4y - 9

⇒ y^{2} + 4y = 5x - 9

⇒ y^{2} + 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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