Question

If the axes are rotated in anticlockwise through an angle of ${90}^{\circ }$ then the equation $x^2=4ay$ will chane into

• A. $Y^2=4aX$
• B. $X^2=-4aY$
• C. $Y^2=-4aX$
• D. $X^2=4aY$

Answer 1

The correct option is A $Y^2=4aX$

Rotating the coordinate axes by ${90}^{\circ }$ anticlockwise will transform the coordinates as

$x=X\cos \left({90}^{\circ }\right)-Y\sin \left({90}^{\circ }\right)$ and
$y=X\sin \left({90}^{\circ }\right)+Y\cos \left({90}^{\circ }\right)$
$\Rightarrow x=-Y,y=X$

Substituting these values in the given equation
$(-Y{)}^2=4a(X)$

$\Rightarrow Y^2=4aX$

$\therefore$ the general equation is $Y^2=4aX$