Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2009MathematicsCircle

The length of the diameter of the circle which cuts three circles array r x²+y²-x-y-14=0 x²+y²+3 x-5 y-10=0 x²+y²-2 x+3 y-27=0 array orthogonally, is

Options

  1. A8
  2. B6
  3. C4
  4. D2

Correct answer

C. 4

Step-by-step solution

Let the equation of circle be x²+y²+2 g x+2 f y+c=0 and centre (-g,-f) Centres of given circles are C ₁ ( 1 2 , 1 2 ), C ₂ (- 3 2 , 5 2 ), C ₃ (1,- 3 2 ) Since, the Eq. (A) cut the given circles orthogonally. array lll & -g-f=c-14 & ( i) & 3 g-5 f=c-10 & ( (ii) and & -2 g+3 f=c-27 & (iii) array On solving Eqs. (i), (ii) and (iii), we get g=-3, f=-4, c=21 From Eq. (A), the circle is x²+y²-6 x-8 y+21=0 Length of diameter =2 (-3)²+(-4)²-21 =4

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 KCET PYQs