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 $ax+by+c=0$ and the curve $x+2y^2=0$ 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
$\therefore a=a,b=ar,c=a{r}^2$
Therefore, given line becomes
$ax+ary+a{r}^2=0$
$\Rightarrow x+ry+r^2=0$
$\Rightarrow x=-ry-r^2\dots (i)$
On putting $x=-ry-r^2$ in given curve
$x+2y^2=0$, we get
$\Rightarrow -ry-r^2+2y^2=0$
$\Rightarrow 2y^2-ry-r^2=0$
$\therefore$ Sum of ordinates $=\frac{r}{2}$