Q â€‹2x+y=7 is one of the bisectors of the angles between the lines represented by αx-22+2γx-2y-3+βy-32=0 - Maths - Straight Lines

Question

Q â€‹2x+y=7 is one of the bisectors of the angles
between the lines represented by
α x - 2 2 + 2 γ x - 2 y - 3 + β y - 3 2 = 0 Then
find the intercepts made by the other bisector on x-axis and y-axis
respectively

Neha Sethi · Accepted Answer

Dear student
Since the two bisectors are perpendicular
The equation of the given bisector is 2x+y-7=0i
e y=-2x+7The slopem of the given bisector is -2Therefore, the slopeM of the other bisector is -1m=12The given equation of pair of straight lines is αx-22+2γx-2y-3+βy-32=0     
(1)The intersection point of the pair of straight line is given by substituting x-2=0 and y-3=0i
e x=2 and y=3The lines are concurrent at (2,3)The angle bisector of the straight lines will also pass through the point (2,3)Therefore, the other bisector passes through the point (2,3) and slope is 12Thus, the equation of the other bisector is y-3=12(x-2)⇒2y-6=x-2⇒x-2y+4=0To find x-intercept,set y=0x+4=0⇒x=-4To find y-intercept,set x=0-2y+4=0⇒2y=4⇒y=2So,(a) is the correct option
Regards

Q. ​2x+y=7 is one of the bisectors of the angles between the lines represented by α x - 2 2 + 2 γ x - 2 y - 3 + β y - 3 2 = 0 . Then find the intercepts made by the other bisector on x-axis and y-axis respectively.

Q. 2x+y=7 is one of the bisectors of the angles between the lines represented by
$α {(x - 2)}^{2} + 2 γ (x - 2) (y - 3) + β {(y - 3)}^{2} = 0$ . Then find the intercepts made by the other bisector on x-axis and y-axis respectively.