The equation -beginvmatrix5 - x - 4 y 12 -5 -1218083lend vmatrix -21 represents a -

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Equation of a Line Passing through 2 Points

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The equation $∣ ∣ ∣ ∣ \begin{matrix} 5 & x & 4 y 2 & - 5 & - 12 1 & 0 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 21$ represents a –

A point on xy plane

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A straight line

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A plane

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None of these

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The equation $∣ ∣ ∣ ∣ \begin{matrix} 5 & x & 4 y 2 & - 5 & - 12 1 & 0 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 21$ represents a –

∣ ∣ ∣ ∣ \begin{matrix} 2 & 1 & 1 1 & 1 & - 1 y & x^{2} & x \end{matrix} ∣ ∣ ∣ ∣

A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3})

∣ ∣ ∣ ∣ \begin{matrix} x & y & 1 x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ \begin{matrix} x & y & 1 x_{1} & y_{1} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0

∣ ∣ ∣ ∣ \begin{matrix} x & 3 & 5 2 & 6 & 10 7 & 21 & 35 \end{matrix} ∣ ∣ ∣ ∣ = 0

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