Question

If $a, b$ and $c$ form a geometric progression with common ratio $r$, then the sum of the ordinates of the points of intersection of the line $a x+b y+c=0$ and the curve $x+2 \,y^{2}=0$ is

• A. $-\frac{r^{2}}{2}$
• B. $-\frac{r}{2}$
• C. $\frac{r}{2}$
• D. r

Answer 1

Answer: (C)

Since, $a, b$ and $c$ form a geometric progression
$\therefore a=a, b=a r, c=a r^{2}$
Therefore, given line becomes
$a x+a r y+a r^{2}=0$
$\Rightarrow x+r y+r^{2}=0$
$\Rightarrow x=-r y-r^{2} \ldots( i )$
On putting $x=-r y-r^{2}$ in given curve
$x+2 y^{2}=0$, we get
$\Rightarrow -r y-r^{2}+2 y^{2}=0 $
$\Rightarrow 2 y^{2}-r y-r^{2}=0$
$\therefore $ Sum of ordinates $=\frac{r}{2}$