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JEE MATHEMATICS MCQ: PAIR OF STRAIGHT LINES

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Two lines represented by the equation x2−y2−2x+1=0x^2-y^2-2 x+1=0 are rotated about the point (1,0)(1,0), the line making the bigger angle with the positive direction of the xx-axis being turned by 45∘45^{\circ} in the clockwise sense and the other line being turned by 15∘15^{\circ} in the anticlockwise sense. The combined equation of the pair of lines in their new position, is
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Correct option: B
3x2−xy−23x+y+3=0\sqrt{3} x^2-x y-2 \sqrt{3} x+y+\sqrt{3}=0
Option B (3x2−xy−23x+y+3=0\sqrt{3} x^2-x y-2 \sqrt{3} x+y+\sqrt{3}=0) is correct because it represents the combined equation of the rotated lines after adjusting their angles with the x-axis.

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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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