(A) Let the point be $(x, y)$.The area of the triangle with vertices $(x, y)$,$(1, 5)$,and $(3, -7)$ is given by the formula:$\frac{1}{2} |x(5 - (-7))

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(A) Let the point be $(x, y)$.The area of the triangle with vertices $(x, y)$,$(1, 5)$,and $(3, -7)$ is given by the formula:$\frac{1}{2} |x(5 - (-7)) + 1(-7 - y) + 3(y - 5)| = 21$$\frac{1}{2} |x(12) - 7 - y + 3y - 15| = 21$$\frac{1}{2} |12x + 2y - 22| = 21$$|6x + y - 11| = 21$This gives two possible equations:$6x + y - 11 = 21 \implies 6x + y - 32 = 0$$6x + y - 11 = -21 \implies 6x + y + 10 = 0$Comparing with the given options,the locus is $6x + y - 32 = 0$.

Class 11 Mathematics Straight Lines Locus of Point

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The point moves such that the area of the triangle formed by it with the points $(1, 5)$ and $(3, -7)$ is $21$ sq. units. The locus of the point is:

A
$6x + y - 32 = 0$
B
$6x - y + 32 = 0$
C
$x + 6y - 32 = 0$
D
$6x - y - 32 = 0$

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Straight Lines

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Locus of Point

$A$ 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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MediumAP EAMCET 2021

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EasyAP EAMCET 2020

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$A$ light ray emerging from the point source placed at $P(1, 3)$ is reflected at a point $Q$ on the $x$-axis. If the reflected ray passes through the point $R(6, 7)$,then the abscissa of $Q$ is

DifficultJEE MAIN 2013

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The point moves such that the area of the triangle formed by it with the points $(1, 5)$ and $(3, -7)$ is $21$ sq. units. The locus of the point is:

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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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