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JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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Application +4 | -1
If one of the lines of the pair ax2+2a x^2+2 hxy +by2=0+b y^2=0 bisects the angle between positive direction of the axes, then a, b and h satisfy the relation.
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Correct option: B
a+b=−2ha+b=-2 h
Option B (a+b=−2ha+b=-2 h) is correct because substituting y=xy=x into the equation and simplifying leads to the relation a+b=−2ha+b=-2h.

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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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