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COMEDK2020MathematicsCircle

The equation to two circles which touch the Y -axis at (0,3) and make an intercept of 8 units on X -axis are

Options

  1. Ax²+y² 6 x-10 y+9=0
  2. Bx²+y² 10 x-6 y+9=0
  3. Cx²+y²+10 x 6 y+9=0
  4. Dx²+y²-8 x 10 y+9=0

Correct answer

B. x²+y² 10 x-6 y+9=0

Step-by-step solution

Equation of circle will be (x a)²+(y-3)²=a² Now, in A C D , aligned & A C²=A D²+C D² a²=(4)²+(3)² & [ A C=a, A D= 1 2 A B=4, C D=3 ] & a²=25 a=5 aligned So, equation of circles will be aligned (x 5)²+(y-3)² &=5² x² 10 x+25+y²-6 y+9 &=25 x²+y² 10 x-6 y+9 &=0 aligned

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