lf the equation $(2 x - y - 3)^{2} = - 20 (x + 2 y - 4)$ represents a parabola then its vertex is

(3, - 3)

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(6, - 1)

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(2, 1)

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(4, 4)

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Solution

The correct option is B $(2, 1)$
Comparing given equation with standard form of parabola, $Y^{2} = - 4 a X$
$X = x + 2 y - 4, Y = 2 x - y - 3 = 0, a = 5$
Clearly the line $X = 0$ and $Y = 0$ are perpendicular to each other.
And we know the vertex of the parabola $Y^{2} = 4 a X$ is $(X = 0, Y = 0)$
Thus the vertex of the given parabola will be the solution of set of
equation $x + 2 y - 4 = 0$ and $2 x - y - 3 = 0$
Solving these we get $x = 2, y = 1$
Hence the vertex of the parabola is $(2, 1)$

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