TS EAMCET 5-Aug-2021 Shift 2 Question Paper

3x+4y=4
Let the coordinates of one point be
(2+r‌cos‌θ,2+r‌sin‌θ)
Then, the coordinates of other point will be
[2+r‌cos(90+θ),2+r‌sin(90+θ)]
⇒‌‌(2−r‌sin‌θ,2+r‌cos‌θ)
Both of the coordinates lie on 3x+4y=4
So, 3(2+r‌cos‌θ)+4(2+r‌sin‌θ)=4
r(3‌cos‌θ+4‌sin‌θ)=−10. . . (i)
And, 3(2−r‌sin‌θ)+4(2+r‌cos‌θ)=4
r(−3‌sin‌θ+4‌cos‌θ)=−10
Divide Eq. (i) by (ii), we get
‌3‌cos+4‌sin‌θ=−3‌sin‌θ+4‌cos‌θ
‌7‌sin‌θ=cos‌θ
‌tan‌θ=1∕7
Hence, slopes are ‌

1

7

and −7.