Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202422 May 2024Morning ShiftMathematicsCircleActual

If A and B are the centres of similitude with respect to the circles x^2+y^2-14 x+6 y+33=0 and x^2+y^2+30 x-2 y+1=0 , then midpoint of AB is

Options

  1. A( 7 3 , 4 5 )
  2. B( 3 2 , 1 5 )
  3. C( 39 2 , -7 4 )
  4. D( 39 4 , -7 2 )

Correct answer

D. ( 39 4 , -7 2 )

Step-by-step solution

aligned & S₁ x^2+y^2-14 x+6 y+33=0 & C₁=(7,-3), r₁= 49+3-33 =5 & S₂ x^2+y^2+30 x-2 y+1=0 & C₂=(-15,1), r₂= 225+1-1 =15 aligned Let A divides C₁ C₂ in r₁: r₂ internally A= ( 21-15 4 , 1-9 4 )= ( 3 2 ,-2 ) Let B divides C₁ C₂ in r₁: r₂ externally B= ( -21-15 1-3 , 1+9 1-3 )=(18,-5) Midpoint of A B= ( 18+ 3 2 2 , -5-2 2 )= ( 39 4 , -7 2 )

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