TS EAMCET 20-July-2022 Shift 1 Solved Paper

According to the question,Let A(a,b),B(0,0),C(c,0) Since, P divides AB in ratio 1:2.
So, ‌‌P(‌

2a

3

,‌

2b

3

)
and Q divides line BC in ratio 1:2.
So,
Q(‌

c

3

,0)
Let D divides AQ line in ratio λ2:1.
Then, y coordinate of D:‌

b

λ2+1

.....(i)
and also let D divides line PC into λ1:1 ratio they y coordinate of D:‌

2b

3(λ1+1)

......(ii)
From Eqs. (i) and (ii), we get
‌‌

b

λ2+1

=‌

2b

3(λ1+1)

⇒‌‌3λ1+3=2λ2+2
⇒‌‌3λ1−2λ2+1=0.....(iii)
also x-coordinate will be equal
⇒λ1=‌

2λ2

9

on putting in Eq. (iii),
‌

2λ2

3

−2λ2+1=0
⇒‌‌‌

−4λ2

3

=−1⇒λ2=‌

3

4

,λ1=‌

1

6

Now,