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JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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Application +4 | -1
If 2x2+7xy+3y2+8x+14y+Ξ»=02 x^2+7 x y+3 y^2+8 x+14 y+\lambda=0 represents a pair of straight lines, find Ξ»\lambda.
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Correct option: A
8
Option A (8) is correct because it is the value of Ξ»\lambda that makes the given equation represent a pair of straight lines, derived by applying the condition abc+2fghβˆ’af2βˆ’bg2βˆ’ch2=0abc + 2fgh - af^2 - bg^2 - ch^2 = 0.

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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 (βˆ’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+2Ξ»xyβˆ’7y2=04 x^2+2 \lambda x y-7 y^2=0 is equal to the product of the slopes, then Ξ»\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 3x2βˆ’3hxy+4y2=03 x^2-3 h x y+4 y^2=0 represents a pair of coincident lines are
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