AP EAMCET20225 Jul 2022Evening ShiftMathematicsCircleActual
The circle touching the y -axis at a distance 4 units from the origin and cutting off an intercept 6 from x -axis is
Options
- Ax^2+y^2 10 x-8 y+16=0
- Bx^2+y^2 5 x-8 y+16=0
- Cx^2+y^2 5 x-2 y-8=0
- Dx^2+y^2 2 x-y-12=0
Correct answer
A. x^2+y^2 10 x-8 y+16=0
Step-by-step solution
The given situation is possible with the 2 circles. Considering centre at C₁x intercept = PQ =6y intercept =0 for x^2+y^2+2 g x+2 f y+c=0 ...(i) x intercept =2 g^2-c =6g^2-c=9y intercept =2 f^2-c =0f^2= c aligned & PB =1 / 2 PQ =3 & OA = C ₁ ~B =4 aligned In p C₁ ~B , PC ₁== C₁ B^2+p B^2 = 3^2+4^2 PC ₁=5 radius of circle =5 radius = g^2+f^2-c g^2+f^2-c=25 aligned & f^2=c & g^2=25 & g= 5 & g^2-c=9 & f^2+9=25 & f^2=16 & f= 4 aligned and c=f^2=16 Equation of circle is x^2+y^2 10 x 8 y+16=0 In given option correct is x