JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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If the pairs of straight lines

a x^2+2 h x y-a y^2=0

and

b x^2+2 g x y-b y^2=0

be such that each bisects the angles between the other, then

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Correct option: A

h g+a b=0

Option A (

h g+a b=0

) is correct because it represents the condition where each pair of lines bisects the angles between the other, leading to a specific relationship between their coefficients.

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

represents parallel straight lines, then Image of the point

(-1,3)

with respect to the line

y=2 x

is If the pair of lines represented by

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

intersect on

y

-axis, then If the sum of the slopes of the lines given by

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

is equal to the product of the slopes, then

\lambda

is equal to The equation

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

represents a pair of straight lines passing through the origin. The two lines are The value of

h

for which

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

represents a pair of coincident lines are