Question

The line x - 2y = 2 intersects the curve x + y2 = 10 at two points A and B. Find the equation of the perpendicular bisector of the line AB.​

Answer 1

x - 2y = 2. …………(1). and x + y^2 =10. ………………(2).

Subtracting eqn. (1) from eqn. (2).

y^2 + 2y = 8.

or, y^2 +2y - 8 =0.

or, (y +4).(y-2)=0.

or, y = -4 , 2. and x = -6 , 6.

Thus, A(-6,-4) and B(6,2). let the mid point of AB is M , M((-6+6)/2,(-4+2)/2)

or, M(0, -1).

slope of AB = (2+4)/(6+6) = 1/2.

Slope of the perpendicular bisector of the line AB= -2.

Hence, the eqn. of the perpendicular bisector of AB is:-

y. +1 = - 2.(x - 0).

or, 2.x + y + 1 = 0. Answer.