Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202018 Sep 2020Morning ShiftMathematicsCircleActual

The radical centre of the circles (x^2+y^2-4 x-6 y+5=0 ), (x^2+y^2-2 x-4 y-1=0 ) and (x^2+y^2-6 x-2 y=0 ) is equal to

Options

  1. A( ( 33 4 , 20 3 ) )
  2. B( ( 33 4 , 10 3 ) )
  3. C( ( 33 4 , -20 3 ) )
  4. D( ( 7 6 , 11 6 ) )

Correct answer

D. ( ( 7 6 , 11 6 ) )

Step-by-step solution

Equation of given circles ( aligned & S₁: x^2+y^2-4 x-6 y+5=0 & S₂: x^2+y^2-2 x-4 y-1=0 aligned ) and ( S₃: x^2+y^2-6 x-2 y=0 ) ( ) Radical axis of circles (S₁ ) and (S₂ ) is (2 x+2 y-6=0 x+y=3 )...(i) Similarly, the radical axis of circles (S₂ ) and (S₃ ) is (-4 x+2 y+1=0 )...(ii) ( ) Radical centre is point of concurrency of radical axes, from radical axes Eqs. (i) and (ii), we get (y= 11 6 and x= 7 6 ) ( ) Radical centre is ( ( 7 6 , 11 6 ) )

Practice Circle on Quantrex Academy →

More from Circle

A circle touches both the coordinate axes and the straight line L 4 x +3 y -6=0 in the first quadrant. If this circle lies below the line L =0 , then the equation of that circle is 2025If the smallest circle through the points of intersection of x^2+y^2=a^2 and x +y =p, 0 < p < a is x^2+y^2-a^2+ (x +y -p)=0 then = 2025If the lines 3 x-4 y+4=0 and 6 x-8 y-7=0 are the tangents to the same circle, then the area of that circle (in sq.units) is 2025Circles are drawn through the point (2,0) to cut intercepts of length 5 units on the X -axis. If their centre lie in the first quadrant, then their equation is 2025The circles x^2+y^2-2 x-4 y-4=0 and x^2+y^2+2 x+4 y-11=0 2025If the line 4 x-3 y+7=0 touches the circle x^2+y^2-6 x+4 y-12=0 at ( , ) , then +2 = 2025The slope of the common tangent drawn to the circles x^2+y^2-4 x+12 y-216=0 and x^2+y^2+6 x-12 y+36=0 is 2025If r₁ and r₂ are radii of two circles touching all the four circles (x r)^2+(y r)^2=r^2 , then r₁+r₂ r = 2025 Full Circle list All AP EAMCET PYQs