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The centroid of the triangle formed by t...

The centroid of the triangle formed by the pair of straight lines `12x^2- 20xy+7y^2=0` and the line `2x-3y + 4 = 0 `is

A

`(-(7)/(3),(7)/(3))`

B

`(-(8)/(3),(8)/(3))`

C

`((8)/(3),(8)/(3))`

D

`((4)/(3),(4)/(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
The separate equation of pair of straight lines of `12x^2-20xy+7y^2=0` are `6x-7y=0 and 2x-y=0`
The , equation of sides of triangle are
`6x-7y=0` ..(i)
`2x-y=0` ..(ii)
and `2x-3y+4=0`........(iii)
On solving these equations , we get the vertices of a triangle i.e., `(0,0) ,(1,2) and (7,6)`.
`therefore` Centroid of triangle is `((0+1+7)/(3),(0+2+6)/(3))=((8)/(3),(8)/(3))`
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