(D) If the equation of a curve $f(x, y) = 0$ remains unchanged when $x$ and $y$ are interchanged,it means $f(x, y) = f(y, x)$.This property implies th

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Symmetric along the line $y = x$

(D) If the equation of a curve $f(x, y) = 0$ remains unchanged when $x$ and $y$ are interchanged,it means $f(x, y) = f(y, x)$.This property implies that for every point $(a, b)$ on the curve,the point $(b, a)$ is also on the curve.The set of points $(a, b)$ and $(b, a)$ are reflections of each other across the line $y = x$.Therefore,the curve is symmetric with respect to the line $y = x$.

Class 11 Mathematics Straight Line Locus of Point

Medium

If the equation of a curve remains unchanged by replacing $x$ with $y$ and $y$ with $x$,then the curve is

A
Symmetric along the $x$-axis
B
Symmetric along the $y$-axis
C
Symmetric along the line $y = -x$
D
Symmetric along the line $y = x$

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Class 11 Questions

Class 11

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Chapter

Straight Line

Subtopic

Locus of Point

$A(-4,0)$ and $B(4,0)$ are two fixed points. $C$ and $D$ are two points on the $Y$-axis such that $CD=4$ and $C$ is a point below $D$. Then the locus of the point of intersection of the lines $AC$ and $BD$ is

MediumTS EAMCET 2022

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The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA$ is equal to:

DifficultAP EAMCET 2003

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Suppose a point $P$ moves so that $BP^2 - AP^2 = 121$,where $A$ and $B$ are $(2, 5)$ and $(5, 11)$ respectively. Then the locus of $P$ is a straight line,whose slope is

MediumAP EAMCET 2022

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The ends of a rod of length $l$ move on two mutually perpendicular lines. The locus of the point on the rod which divides it in the ratio $1 : 2$ is

MediumIIT 1987

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$A$ point $P$ moves inside a square of area $4$ square units such that it is nearer to the point of intersection of its diagonals than any vertex. The area of the region traced by $P$ is

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If the equation of a curve remains unchanged by replacing $x$ with $y$ and $y$ with $x$,then the curve is

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$A(-4,0)$ and $B(4,0)$ are two fixed points. $C$ and $D$ are two points on the $Y$-axis such that $CD=4$ and $C$ is a point below $D$. Then the locus of the point of intersection of the lines $AC$ and $BD$ is

The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA$ is equal to:

Suppose a point $P$ moves so that $BP^2 - AP^2 = 121$,where $A$ and $B$ are $(2, 5)$ and $(5, 11)$ respectively. Then the locus of $P$ is a straight line,whose slope is

The ends of a rod of length $l$ move on two mutually perpendicular lines. The locus of the point on the rod which divides it in the ratio $1 : 2$ is

$A$ point $P$ moves inside a square of area $4$ square units such that it is nearer to the point of intersection of its diagonals than any vertex. The area of the region traced by $P$ is

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