# if a, b and c from G.P with common ration r ,the sum of the y cordinates of the points of intersection of the line ax+by+c=0 and the curve $x+2y^{2}=0$ is Option 1) $-\frac{r}{4}$ Option 2) $-\frac{r}{2}$ Option 3) $\frac{r}{2}$ Option 4) $\frac{r}{4}$

As learnt in

General term of a GP -

$T_{n}= ar^{n-1}$

- wherein

$a\rightarrow$ first term

$r\rightarrow$ common ratio

And,

$ax+by+c=0$

$b=ar, c=ar^{2}$

$x+ry+r^{2}=0$

Also,

$x+2y^{2}=0$

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

$Sum= \frac{r}{2}$

Option 1)

$-\frac{r}{4}$

This option is incorrect.

Option 2)

$-\frac{r}{2}$

This option is incorrect.

Option 3)

$\frac{r}{2}$

This option is correct.

Option 4)

$\frac{r}{4}$

This option is incorrect.

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