Question

The ordinate of a point P is three times its abcissae, P lies on

Answer 1

Let P$(x,3x)$
A) Substituting $y=3x$ in $y^2=45x\Rightarrow 9x^2-45x=0\Rightarrow 9x(x-5)$
We get coordinates of P as $(0,0)(5,15)$
B) Substituting $y=3x$ in $y^2=45x\Rightarrow 9x^2-45x=0\Rightarrow 9x(x-5)$
We get coordinates of P as $(0,0),(3,9)$
C) Substituting $y=3x$ in $\frac{x^2}{9}+\frac{y^2}{81}=2\Rightarrow \frac{x^2}{9}+\frac{9x^2}{81}=2\Rightarrow \frac{2x^2}{9}=2$
$\Rightarrow x^2=9\Rightarrow x=\pm 3$
We get coordinates of P as $(3,9),(-3,-9)$
D) Substituting $y=3x$ in $\frac{2x^2}{25}-\frac{y^2}{225}=1\Rightarrow \frac{2x^2}{25}-\frac{{9x}^2}{225}=1\Rightarrow \frac{2x^2}{25}-\frac{x^2}{25}=1$
$\Rightarrow \frac{x^2}{25}=1\Rightarrow x^2=25\Rightarrow x=\pm 5$
We get coordinate of P as $(5,15)(-5,-15)$