Question

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

Solution

Correct option is

–15

Equation of bisectors of angle between 3x2 – 2pxy – 3y2 = 0 is

  

Comparing with 5 (x2 – y2) – 2qxy = 0, p = –5, q = 3  

SIMILAR QUESTIONS

Q1

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

Q2

The straight lines 4x – 3y – 5 = 0, x – 2y – 10 = 0, 7x + 4y – 40 = 0 and x + 3y + 10 = 0 form the sides of a

Q3

If two vertices of a triangle are (5, –1) and (–2, 3), and the orthocenter lies at the origin, the coordinate of the third vertex are 

Q4

 

Equation of a line passing through the intersection of the lines

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

Q5

 The lengths of the perpendicular from the points (m2, 2m), (mmm +m) and (m2, 2m) to the line x + y + 1 = 0 form

Q6

The sine of the angle between the pair of lines represented by the equation x2 – 7xy + 12y2 = 0 is 

Q7

The square of the differences of the slopes of the lines represented by the equation x2(sec2θ – sin2θ) – (2xy tan θ + y2 sin2θ = 0) is 

Q8

The line joining the origin to the points of intersection of x2 + y2 + 2gx + c = 0 and x2 + y2 + 2fy – c = 0 are at right angles, if

Q9

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

Q10

The line x + y = 1 meets the line represented by the equation y3 –xy2 – 14x2y + 24x3 = 0 at the points ABC. If O is the origin, then

OA2 + OB2 + OC2 is equal to