TS EAMCET 19-July-2022 Shift 1 Solved Paper

The two given lines 2x−3y+4=0 and 6x−9y+7=0 are parallel.Slope of these lines =‌

2

3

and slope of line L=‌

−3

2

Equation of line L is
‌y−1=‌

−3

2

(x−1)
‌2y−2=−3x+3
‌3x+2y=5
Solving equation 3x+2y=5 and 2x−3y+4=0 to determine the point A.
x=‌

7

13

,y=‌

22

13

Solving equation 3x+2y=5 and 6x−9y+7=0 to get the point B.
x=‌

31

39

and y=‌

17

13

∴ Coordinates of point A is (‌

7

13

,‌

22

13

) and point B is
(‌

31

39

,‌

17

13

)
Let P divides in the ratio K:1
‌1=‌

K× 31 39 +1× 7 13

K+1

‌⇒‌‌39(K+1)=31K+21
‌⇒‌‌39K+39=31K+21
‌⇒‌‌8K=−18
‌K=‌

−9

4

∴P divides AB in the ratio 9:4 externally.