O is the origin and A is the point (3,4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is

4x - 3y = 0

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4x + 3y = 0

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3x + 4y = 0

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3x - 4y = 0

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Solution

The correct option is A
4x - 3y = 0

Since OA and OP will be parallel only when O, A and P are collinear.

Therefore, $∣ ∣ ∣ ∣ \begin{matrix} 0 & 0 & 1 3 & 4 & 1 x & y & 1 \end{matrix} ∣ ∣ ∣ ∣$ = 0 $\Rightarrow$ 4x - 3y = 0.

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