Two Of The Lines Represented By x3 – 6x2y + 3xy2 + dy3 = 0 Are Perpendicular For   

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Question

Two of the lines represented by x3 – 6x2y + 3xy2 + dy3 = 0 are perpendicular for   

Solution

Correct option is

Two real values of d

Product of the slopes is given by m1m2m3 = –1/d.

If m1 m2 = –1, then m3 = 1/d and m3 satisfies the equation

    dm3 + 3m3 – 6m + 1 = 0  

⇒ d2 – 6d + 4 = 0 which gives two real values of d. 

Testing

SIMILAR QUESTIONS

Q1

If p1p2 denote the lengths of the perpendiculars from the origin on the lines x sec α + y cosec α = 2a and

x cos α + y sin α = a cos 2α respectively, then  is equal to

Q2

The locus of the point of intersection of the lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ) y + a sin θ = 0 is

Q3

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Q4

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Q5

 

Equation of a line passing through the intersection of the lines

x + 2y – 10 = 0 and 2x + y + 5 = 0 is 

Q6

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Q7

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Q8

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Q9

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Q10

If pairs of lines 3x2 – 2pxy – 3y2 = 0 and 5x2 – 2qxy – 5y2 = 0 are such that each pair bisects the angle between the other pair, then pq is equal to