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Paragraph: The circle x^2+y^2-8 x=0 and hyperbola x^2 9 - y^2 4 =1 intersect at the points A and B . Question: Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

Options

  1. A2 x- 5 y-20=0
  2. B2 x- 5 y+4=0
  3. C3 x-4 y+8=0
  4. D4 x-3 y+4=0

Correct answer

B. 2 x- 5 y+4=0

Step-by-step solution

Equation of tangent to hyperbola having slope m is y=m x+ 9 m^2-4 Equation of tangent to circle is y=m(x-4)+ 16 m^2+16 Eqs. (i) and (ii) will be identical for m= 2 5 satisfy. Equation of common tangent is 2 x- 5 y+4=0

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