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VITEEE2007MathematicsThree Dimensional Geometry

The length of the straight line x -3 y =1 intercepted by the hyperbola x²-4 y²=1 is

Options

  1. A10
  2. B6 5
  3. C1 10
  4. D6 5 10

Correct answer

D. 6 5 10

Step-by-step solution

Given : equation of line, x-3 y=1 (1) and hyperbola x²-4 y²=1 (2) putting x=1+3 y in equation (2) , we get array l (1+3 y)²-4 y²=1 1+9 y²+6 y-4 y²=1 5 y²+6 y=0 y(5 y+6)=0 y=0 or y=- 6 5 x=1 for y=0 & x=1- 18 5 = -13 5 array for y=-6 / 5 the line (1) cuts the hyperbola (2) in at most two point. co-ordinates of points are P (1,0) & array l Q (- 13 5 ,- 6 5 ) PQ = (1+ 13 5 )²+ (0+ 6 5 )² array = ( 18 5 )²+ 36 25 = 324+36 25 = 360 25 length of straight line PQ = 6 10 5 units.

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