Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2016MathematicsCircle

If ( x=2+3 ) and ( y=1-3 ) represent a circle then the centre and radius is

Options

  1. A( (2,1), 9 )
  2. B( (2,1), 3 )
  3. C( (1,2), 1 3 )
  4. D( (-2,-1), 3 )

Correct answer

B. ( (2,1), 3 )

Step-by-step solution

Given that, x=2+3 (1)y=1-3 (2) From Eqs. (1) and (2) , we have x-2 3 = and y-1 -3 = We know that, ² + ² =1 So, ( x-2 3 )²+ ( y-1 -3 )=1 (x-2)² 9 + (y-1)² 9 =1 (x-2)²+(y-1)²=9 So, it is circle centre at point (2,1) and radius is 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 KCET PYQs