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Question

6. 2x + y = 7 is one of the bisectors of the angles between the lines represented by α(x – 2)2 + 2γ(x – 2) (y – 3) + β(y – 3)2 = 0. Then the intercepts made by the other bisector on the x-axis and y-axis respectively.
(a) –4, 2 (b) 4, –2 (c) 2, –4 (d) –2, 4

7. If A(1, 2) and B(4, 3) are two points, then a point P on the line 3x – 4y + 7 = 0 such that |AP – PB| is maximum, is
(a) 85, 15 (b) -15, 85 (c) 85, -15 (d) 15, 35

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Solution

Dear student
The equation of the given bisector is 2x+y=7y=-2x+7The slope of the given bisector is -2Therefore the slope of the other bisector is 12The given equation of pair of straight lines isαx-22+2γ(x-2)(y-3)+β(y-3)2=0 ...(1)The intersection point of the pair of straight line is given by substitutingx-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 12.Thus, the equation of the other bisector isy-3=12(x-2)2y-6=x-2x-2y+4=0 ...(A)So, x-intercept is -4 (on putting y=0 in (A))y-intercept is 2 (on putting x=0 in (A))
Regards

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