The focus of the parabola 4y^2 - 6x - 4y = 5 | vedclass

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Question

(B) Given equation of the parabola: $4y^2 - 4y - 6x = 5$Completing the square for $y$: $4(y^2 - y) = 6x + 5$$4(y^2 - y + 1/4) = 6x + 5 + 1$$4(y - 1/2)

Vedclass · Accepted Answer

$(-5/8, 1/2)$

Vedclass · Answer

(B) Given equation of the parabola: $4y^2 - 4y - 6x = 5$Completing the square for $y$: $4(y^2 - y) = 6x + 5$$4(y^2 - y + 1/4) = 6x + 5 + 1$$4(y - 1/2)^2 = 6(x + 1)$$(y - 1/2)^2 = \frac{3}{2}(x + 1)$Comparing with the standard form $Y^2 = 4aX$,where $Y = y - 1/2$,$X = x + 1$,and $4a = 3/2$.Thus,$a = 3/8$.The focus in the $(X, Y)$ coordinate system is $(a, 0) = (3/8, 0)$.Converting back to $(x, y)$ coordinates:$x + 1 = 3/8 \Rightarrow x = -5/8$$y - 1/2 = 0 \Rightarrow y = 1/2$Therefore,the focus is $(-5/8, 1/2)$.

The focus of the parabola $4y^2 - 6x - 4y = 5$ is

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