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Rectangular Cartesian Coordinate System

If the distan...

Question

If the distance between the points $(2, 1)$ and $(α, 3)$ is equal to minimum value of the quadratic equation $y = x^{2} - 4 x + 6$ i.e. $β$ and which is possible at $x = γ$ , then $α + β + γ$ is:

4

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6

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8

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Solution

The correct option is C $6$
$y = x^{2} - 4 x + 6 \Rightarrow (x - 2)^{2} + 2$
$∴ y_{m i n i} = 2 = β$
which is possible at $x = 2 = γ$
Now, distance between $(2, 1)$ and $(α, 3)$ is
$\sqrt{(α - 2)^{2} + 4} = β = 2 \Rightarrow α = 2$
$∴ α + β + γ = 6$

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