AP EAMCET202120 Aug 2021Morning ShiftMathematicsPair of LinesActual
The equation of bisectors of the angle between the lines represented by 3 x 2 - 5 x y + 4 y 2 = 0 is
Options
- A9 x 2 + 6 y 2 - 2 x = 0
- B5 x 2 - y 2 = 2 x y
- C3 x 2 + 2 x y - y 2 = 0
- D5 x 2 + x y + 4 y 2 = 0
Correct answer
B. 5 x 2 - y 2 = 2 x y
Step-by-step solution
Given equation is 3 x 2 - 5 x y + 4 y 2 = 0             . . . . . 1 Compare the given equation with a x 2 + 2 h x y + b y 2 = 0           . . . . . . 2 We get, a = 3 ,   2 h = - 5 and b = 4 Now the equation of the bisector of the angle between the pair of lines 1 is x 2 - y 2 a - b = x y h ⇒ x 2 - y 2 3 - 4 = x y - 5 2 ⇒   5 x 2 - 2 x y - 5 y 2 = 0 ⇒ 5 x 2 - y 2 = 2 x y