TS EAMCET 20-July-2022 Shift 1 Solved Paper

x-intercept of line =5
So, a=5(5,0).
y-intercept of line =7
So, b=7(0,7)
Equation of line : ‌

x

a

+‌

y

b

=1
⇒‌‌‌

x

5

+‌

y

7

=1
Equation of line w.r.t. old axis : 7x+5y=35 Now replace x→x‌cos‌θ−ysin‌θ,
y→xsin‌θ+y‌cos‌θ
Equation of line L w.r.t. new axis
For x-intercept, on putting x=0,x-intercept
=‌

35

7‌cos‌θ+5sin‌θ

For y-intercept, on putting x=0,
y-intercept =‌

35

5‌cos‌θ−7sin‌θ

Given, x-intercept =y-intercept
‌∴7‌cos‌θ+5sin‌θ=5‌cos‌θ−7sin‌θ
‌⇒‌‌tan‌θ=−‌

1

6

‌∴‌‌|tan‌θ|=‌

1

6