If θ 1 and θ 2 be the angles which the lines (x 2 + y 2 ) (…

Maths Straight Line Mix Single Correct MCQ

Published on: August 14, 2026

If θ 1 and θ 2 be the angles which the lines (x 2 + y 2 ) (cos 2 θ sin 2 α + sin 2 θ ) = (x tan α – y sin θ ) 2 make with the axis of x,

and θ = , then tan θ 1 + tan θ 2 is equal to -

–

sin α

–

cosec 2 α

–

cosec 2 α

–4cosec 2 α

Text Solution

Verified by Experts

The correct answer is:

The given equation can be written as

(x 2 + y 2 ) (cos 2 θ sin 2 α + sin 2 θ ) = x 2 tan 2

α – 2xy tan α sin θ + y 2 sin 2 θ

or (cos 2 θ sin 2 α + sin 2 θ – tan 2 α )x 2 + 2(tan α sin θ ) xy + cos 2 θ sin 2 α y 2 = 0

Since the slope of these lines are given as tan θ 1 and tan θ 2

Sum of the slopes =

⇒ tan θ 1 + tan θ 2 = = cosec2 α .

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