Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201921 Apr 2019Morning ShiftMathematicsCircleActual

If the point of intersection of the pair of the transverse common tangents and that of the pair of direct common tangents drawn to the circles x^2+y^2-14 x+6 y+33=0 and x^2+y^2+30 x-2 y+1=0 are T and D respectively, then the centre of the circle having TD as diameter is

Options

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

Correct answer

C. ( 39 4 , -7 2 )

Step-by-step solution

Given, C₁: x^2+y^2+30 x-2 y+1=0 aligned & centre (O)=(-15,1) & and radius = 225+1-1 = 225 =15 & and C₂: x^2+y^2-14 x+6 y+33=0 & Centre (O^ )=(7,-3) & and radius = 49+9-33 = 25 =5 aligned Since, point T divides O O^ in 15: 5 i.e., 3: 1 internally. T= ( 21-15 4 , -9+1 4 )= ( 3 2 ,-2 ) Also, point D divides O O^ in 15: 5 i.e., 3: 1 externally. D= ( 21+15 2 , -9-1 2 )=(18,-5) Now, centre of circle with T D as diameters of mid-point of T D = ( 18+3 / 2 2 , -2-5 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