Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2011MathematicsPair of Lines

If the equation 12 x^2+7 x y-p y^2-18 x+q y+6=0 represents a pair of perpendicular straight lines, then

Options

  1. Ap=12, q=-1
  2. Bp=-12, q=1
  3. Cp=12, q=1
  4. Dp=1, q=1

Correct answer

C. p=12, q=1

Step-by-step solution

The second degree equation will represent a pair of perpendicular straight lines, if | array lll a & h & g h & b & f g & f & c array |=0 and a+b=0 Given pair of line is 12 x^2+7 x y-p y^2-18 x+q y+6=0 | array ccc 12 & 7 / 2 & -9 7 / 2 & -p & q / 2 -9 & q / 2 & 6 array |=0 array ll and & 12-p=0 & p=12 array | array ccc 12 & 7 / 2 & -9 7 / 2 & -12 & q / 2 -9 & q / 2 & 6 array |=0 aligned & 12 (-72+ q^2 4 )- 7 2 (-21+ 9 q 2 ) & -9 ( 7 q 4 -108 )=0 & -864-3 q^2- 147 2 - 63 q 4 & - 63 q 4 +972=0 q=1 aligned

Practice Pair of Lines on Quantrex Academy →

More from Pair of Lines

If the angle made by the lines represented by the equation ax^2 + 2hxy + by^2 = 0 with X-axis are and , then ( + ) is 2026If the equation 16x^2 - 24xy + 9y^2 - 8x + 6y - 35 = 0 represents a pair of straight lines, then the equation of the locus of points equidistant from these two lines is.......... 2026If two lines represented by x^2 - (1 + 3 )xy + 3 y^2 = 0 make angles and with the X-axis, then ( + ) is... 2026If the combined equation of angle bisectors of the lines x^2 - 2pxy - y^2 = 0 is x^2 - 2qxy - y^2 = 0 , then which of the following is true? 2026The combined equation of lines parallel to the coordinate axes and passing through the point of intersection of lines represented by x^2 - 6xy + 5y^2 + 10x - 14y + 9 = 0 is 2026Two lines are given by x^2 - 4xy + 4y^2 + kx - 2ky = 0 , then the value of k so that the distance between them is 3 is 2026If the equation ax^2 + 4xy - 2y^2 + 4x + 8y + 1 = 0 represents a pair of straight lines, then the coordinates of their point of intersection are......... 2026The joint equation of a pair of lines passing through point (1,4) , one of which is parallel to X-axis and the other makes an angle of 45^ with the positive direction of X-axis, is 2026 Full Pair of Lines list All Manipal MET PYQs