Advertisement Remove all ads

Find ' ' P and ' ' Q If the Equation - Mathematics and Statistics

Sum

 Find 'p' and 'q' if the equation px2 - 8xy +3y2 +14 x +2y +q = 0 represents a pair of perpendicular lines.

Advertisement Remove all ads

Solution

Given general equation is px2 - 8xy +3y2 +14 x +2y +q = 0

a = p , h = -4 , b = 3 , g = 7, f = 1 , c = q

Since the equation represents perpendicular lines 

a +b =0

p + 3 = 0

∴ p = -3 

∴ a = p = -3

Since the equation represents a pair of lines.

`abs[("a","h" ,"g"),("h","b","f"),("g" ,"f" , "c")] = 0`

`abs[(-3,-4,7),(-4,3,1),(7,1,"q")] = 0`

∴ -3(3q-1)+4(-4q-7)+7(-4-21)=0

∴ -9q +3 -16q - 28 - 28 - 147 = 0

∴ -25q + 3 - 28 - 175 = 0

∴ -25q + 3 - 203 = 0

∴ -25q - 200 = 0

∴ -25q = 200

∴ q = `200/-25`

∴ q = -8

∴ p = -3 , q = -8

Concept: Pair of Straight Lines - Pair of Lines Passing Through Origin - Combined Equation
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×