Question

If $a,b,c$ 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

The correct option is C $\frac{r}{2}$

$b=ar$ and $c=a{r}^2$

Put the value of $b$ and $c$ in equation

$ax+ary+a{r}^2=0$

$\Rightarrow x+ry+r^2=0$

$\Rightarrow x=-ry-r^2$

Now, put the value of $x$ in curve equation

$2y^2-ry-r^2=0$

$\therefore$ Sum of ordinate $=\frac{r}{2}$