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JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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If y=mxy=m x be one of the bisectors of the angle between the lines ax2−2hxy+by2=0a x^2-2 h x y+b y^2=0, then
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Correct option: C
h(1−m2)+m(a−b)=0h\left(1-m^2\right)+m(a-b)=0
Option C, h(1−m2)+m(a−b)=0h(1-m^2)+m(a-b)=0, is correct because it represents the condition when y=mxy=mx is one of the angle bisectors of the given pair of lines.

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If ax2+2hxy+by2+2gx+2fy+c=0a 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)(-1,3) with respect to the line y=2xy=2 x is If the pair of lines represented by ax2+2hxy+by2+2gx+2fy+c=0a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 intersect on yy-axis, then If the sum of the slopes of the lines given by 4x2+2λxy−7y2=04 x^2+2 \lambda x y-7 y^2=0 is equal to the product of the slopes, then λ\lambda is equal to The equation 3x2+2hxy+3y2=03 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 hh for which 3x2−3hxy+4y2=03 x^2-3 h x y+4 y^2=0 represents a pair of coincident lines are
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