Q. 25.0( 2 Votes )

# write the distance between the vertex and focus of the parabola y^{2} + 6y + 2x + 5 = 0

Answer :

Given equation of the parabola is y^{2} + 6y + 2x + 5 = 0

⇒ y^{2} + 6y + 5 = - 2x

⇒ y^{2} + 6y + 9 = - 2x + 4

⇒ (y + 3)^{2} = - 2(x - 2)

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

⇒ 4b = 2

⇒

⇒

We know that the distance between the vertex and focus is b.

∴The distance between the vertex and focus is .

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