Question

At what point of the parabola x^2=9y is the abscissa three times that of ordinate ?

Answer 1

Let the ordinates of the required point is y

$\therefore abscissa=3y\therefore \text{The coordinates of the point are (3y,y)}\text{These point lies on the parabola}{x}^2=9y(3y{)}^2=9y\therefore 9y^2=9y\Rightarrow 9y(y-1)=0\Rightarrow y-1=0[\because y\ne 0]\Rightarrow y=1\therefore abscissa=3\times y=3\text{Hence,the required point is (3,1)}.$