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Give answer! - Algebra - BITSAT-4

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}

 
Answers (2)
115 Views

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.

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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