Question

Identify the true statements in the following :
(i) If a curve is symmetrical about the origin, then it is symmetrical about both the axes.
(ii) If a curve is symmetrical about both the axes, then it is symmetrical about the origin.
(iii) A curve $f(x,y)=0$ is symmetrical about the line $y=x$ if $f(x,y)=f(y,x)$.
(iv) For the curve $f(x,y)=0$ if $f(x,y)=f(-y,-x)$ then it is symmetrical about the origin.

• A. $\left(ii\right),\left(iii\right)$
• B. $\left(i\right),\left(iv\right)$
• C. $\left(i\right),\left(iii\right)$
• D. $\left(ii\right),\left(iv\right)$

Answer 1

The correct option is A $\left(ii\right),\left(iii\right)$

Consider $\left(1\right)$ , The statement need not be true $($For example take $x^2$ , it is symmetric about the origin and symmetric about the $y$ axis but not symmetric about the $x$ axis$)$

Consider $\left(2\right)$ , The statement is always true

Consider $\left(3\right)$ , The statement is always true

Consider $\left(4\right)$ , The statement is false

Therefore the correct option is $A$