Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2024MathematicsCircle

The number of common tangent to the circle x^2+y^2=9 and x^2+y^2-6 x-8 y+21=0

Options

  1. A0
  2. B1
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

If equation of circle is x^2+y^2+2 g x+2 f y+c=0 Then, centre (-g,-f) radius = g^2+f^2-c Centre of first circle (0,0) radius of first circle 3 Centre of second circle (3,4) radius of second circle 9+16-21 =2 Distance between centres of circle (c₁ c₂ ) = 3^2+4^2 =5 Sum of radius (r₁+r₂ )=5 c₁ c₂=r₁+r₂ (circle touches externally) Number of common tangent =3

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 COMEDK PYQs