Question no. 24 Part B
Q.24. (B) If line 2x - by + 1 = 0 intersects the curve 2 x 2 - b y 2 + 2 b - 1 x y - x - b y = 0 at points A & B and AB subtends a right angle at origin, then value of b + b 2 is equal to

Dear Student,
Please find below the solution to the asked query:

This is question of homogenizationWe have2x-by+1=01=by-2x...iNow2x2-by2+2b-1xy-x-by=02x2-by2+2b-1xy-x1-by1=0Use i2x2-by2+2b-1xy-xby-2x-byby-2x=02x2-by2+2b-1xy-bxy+2x2-b2y2+2bxy=04x2+y2-b-b2+2b-1xy-bxy+2bxy=0As line subtend right angle at origin, henceCoefficient of x2+Coefficient of y2=04-b-b2=0b+b2=4

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