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Straight lines

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in Co-ordinate geometry by (15 points)
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O is origin of the point A(3, 4).if the point P moves so that the line segment op is always parallel to the line segment oa then the equation of to the locus of point P is

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

Therefore, \(\begin{vmatrix}0&0&1\\3&4&1\\x&y&1 \end{vmatrix} = 0\)

⇒ 4x - 3y = 0

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