(A) The origin $O$ is $(0,0)$ and point $A$ is $(3,4)$.Since the line segment $OP$ is parallel to $OA$ and both share the common point $O$,the points

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(A) The origin $O$ is $(0,0)$ and point $A$ is $(3,4)$.Since the line segment $OP$ is parallel to $OA$ and both share the common point $O$,the points $O, A,$ and $P$ must be collinear.The slope of line $OA$ is $m = \frac{4-0}{3-0} = \frac{4}{3}$.Since $P(x,y)$ lies on the line passing through $O(0,0)$ with slope $m = \frac{4}{3}$,the equation of the locus is $y - 0 = \frac{4}{3}(x - 0)$.This simplifies to $3y = 4x$,or $4x - 3y = 0$.

Class 11 Mathematics Straight Line Locus of Point

Easy

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

A
$4x - 3y = 0$
B
$4x + 3y = 0$
C
$3x + 4y = 0$
D
$3x - 4y = 0$

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Straight Line

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Locus of Point

If $L : ax + by + c = 0$ is a variable straight line,where $a, b$ and $c$ are the second,fourth,and seventh terms of an $AP$ respectively,then $L$ passes through the fixed point:

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$A$ point on the straight line $3x + 5y = 15$ which is equidistant from the coordinate axes will lie in

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$A$ straight line cuts off intercepts on the coordinate axes,the reciprocal of whose sum is $1/p$. Through which fixed point does this line always pass?

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$A$ line passing through the point $(1, 2)$ meets the axes at $P$ and $Q$ such that it forms a triangle $OPQ$,where $O$ is the origin. If the area of triangle $OPQ$ is minimum,then the slope of the line $PQ$ is:

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The point whose abscissa is equal to its ordinate and which is equidistant from the points $(1, 0)$ and $(0, 3)$ is

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

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If $L : ax + by + c = 0$ is a variable straight line,where $a, b$ and $c$ are the second,fourth,and seventh terms of an $AP$ respectively,then $L$ passes through the fixed point:

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