(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

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Straight Line

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Locus of Point

$A$ straight line meets the $X$ and $Y$ axes at the points $A$ and $B$ respectively. If $AB = 6$ units,then the locus of the point $P$ which divides the line segment $AB$ such that $AP : PB = 2 : 1$ is

MediumAP EAMCET 2019

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$A$ ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The coordinates of the point $A$ are

Difficult

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The coordinates of a point $P$ on the line $2x - y + 5 = 0$ such that $|PA - PB|$ is maximum,where $A$ is $(4, -2)$ and $B$ is $(2, -4)$,are:

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The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

EasyTS EAMCET 2005

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If a variable line drawn through the intersection of the lines $\frac{x}{3} + \frac{y}{4} = 1$ and $\frac{x}{4} + \frac{y}{3} = 1$ meets the coordinate axes at $A$ and $B$ $(A \neq B)$,then the locus of the midpoint of $AB$ is

DifficultJEE MAIN 2016

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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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$A$ straight line meets the $X$ and $Y$ axes at the points $A$ and $B$ respectively. If $AB = 6$ units,then the locus of the point $P$ which divides the line segment $AB$ such that $AP : PB = 2 : 1$ is

$A$ ray of light coming from the point $(1, 2)$ is reflected at a point $A$ on the $x$-axis and then passes through the point $(5, 3)$. The coordinates of the point $A$ are

The coordinates of a point $P$ on the line $2x - y + 5 = 0$ such that $|PA - PB|$ is maximum,where $A$ is $(4, -2)$ and $B$ is $(2, -4)$,are:

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If a variable line drawn through the intersection of the lines $\frac{x}{3} + \frac{y}{4} = 1$ and $\frac{x}{4} + \frac{y}{3} = 1$ meets the coordinate axes at $A$ and $B$ $(A \neq B)$,then the locus of the midpoint of $AB$ is

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