If the acute angles between the pairs of lines $3 x^2-7 x y+4 y^2=0$ and $6 x^2-5 x y+y^2=0$ be $\theta_1$ and $\theta_2$ respectively, then

JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

1 Medium

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Application +4 | -1

If the acute angles between the pairs of lines

3 x^2-7 x y+4 y^2=0

and

6 x^2-5 x y+y^2=0

\theta_1

and

\theta_2

respectively, then

View answer and explanation

Correct option: A

\theta_1=\theta_2

Option A (

\theta_1=\theta_2

) is correct because the acute angles between the pairs of lines are equal.

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a x^2+2 h x y+b y^2+2 g x+2 f y+c=0

(-1,3)

y=2 x

a x^2+2 h x y+b y^2+2 g x+2 f y+c=0

y

4 x^2+2 \lambda x y-7 y^2=0

\lambda

3 x^2+2 h x y+3 y^2=0

h

3 x^2-3 h x y+4 y^2=0