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AP EAMCET202420 May 2024Morning ShiftMathematicsCircleActual

Equation of the circle having its centre on the line 2 x+y+3=0 and having the lines 3 x+4 y-18=0,3 x+4 y+2= 0 as tangents is

Options

  1. Ax^2+y^2+6 x+8 y+4=0
  2. Bx^2+y^2-6 x-8 y+18=0
  3. Cx^2+y^2-8 x+10 y+37=0
  4. Dx^2+y^2+8 x-10 y+37=0

Correct answer

D. x^2+y^2+8 x-10 y+37=0

Step-by-step solution

Equations of tangents 3 x+4 y-18=0 3 x+4 y+2=0 Since slope of tangents are equal. So tangents are parallel. And distance between two parallel lines is d= |c₂-c₁ | a^2+b^2 = 20 5 =4 Radius = 4 2 =2 Let (h, k) be the centre and radius is perpendicular on tangent perpendicular distance from centre to tangent = radius 3 h+4 k+2 5 =2 3 h+4 k-8=0 ....(i) Also (h, k) lies on 2 x+y+3=0 2 h+k+3=0 ...(ii) From (i) and (ii), h=-4, k=5 Equation of circle is x^2+y^2+8 x-10 y+37=0

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