AP EAPCET 23-Aug-2021 Shift 2 Paper

Given θ is the angle between the lines x2+2hxy+by2=0
To find Angle between x2+2xy‌sec‌θ+y2=0
Since, we know that angle between the line ax2+2hxy+by2=0 is
tan‌θ=|

2√h2−ab

a+b

|
Here, a=1
tan‌θ=|

2√h2−b

1+b

| ...(i)
For x2+2xy‌sec‌θ+y2=0
a=1,h=sec‌θ,b=1
Let θ be the angle, then tan‌ϕ=|

2√sec2θ−1

1+1

|
tan‌ϕ=

2‌tan‌θ

2

=tan‌θ
⇒ϕ=θ