Question

If the axes are rotated anticlockwise through an angle ${90}^{\circ }$ then the equation $x^2=4ay$ is changed to the equation

• 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

$x^{\prime }=x\cos \left({90}^{\circ }\right)+y\sin \left({90}^{\circ }\right)$ and $y^{\prime }=-x\sin \left({90}^{\circ }\right)+y\cos \left({90}^{\circ }\right)$

$\Rightarrow x^{\prime }=y,y^{\prime }=-x$

$\Rightarrow y=x^{\prime },x=-y^{\prime }$

Substituting these values in the given equation

$(-y^{\prime }{)}^2=4a(x^{\prime })$

$\Rightarrow y^{\prime 2}=4a{x}^{\prime }$

$\therefore$ the general equation is $y^2=4ax$