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AP EAMCET20226 Jul 2022Evening ShiftMathematicsHyperbolaActual

The distance between the tangent lines to the hyperbola x^2-2 y^2=18 which are perpendicular to the line y=x is

Options

  1. A6
  2. B2 3
  3. C3 2
  4. D0

Correct answer

B. 2 3

Step-by-step solution

The line perpendicular to line y=x is y=-x+c or x+y-c=0 Given, hyperbola is x^2-2 y^2=18 or x^2 18 - y^2 9 =1 Here, a^2=18, b^2=9 Condition for tangency of hyperbola is aligned & c^2=a^2 m^2-b^2 & c^2=18 (-1)^2-9 & c^2=9 c=+3 aligned Equation of tangents are x+y 3=0 aligned Distance between tangent & = |6| 1^2+1^2 & = 6 2 or 3 2 units aligned

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