Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2002MathematicsCircle

A line is at a constant distance c from the origin and meets the coordinate axes in A and B . The locus of the centre of the circle passing through O, A, B is

Options

  1. Ax^2+y^2=c^2
  2. Bx^2+y^2=2 c^2
  3. Cx^2+y^2=3 c^2
  4. Dx^2+y^2=4 c^2

Correct answer

D. x^2+y^2=4 c^2

Step-by-step solution

Let the equation of the circle be x^2+y^2+2 g x+2 f y+c=0 It passes through origin so c=0 Then, the equation of circle is x^2+y^2+2 g x+2 f y=0 It also passes through A (x₁, 0 ) array rlrl & x₁^2+0+2 g x₁ & =0 & & g & =- x₁ 2 array It also passes through B (0, y₁ ) o+y₁^2+2 f y₁=0 f= -y₁ 2 centre of the circle is ( x₁ 2 , y₁ 2 ) Mid point of A B is ( x₁ 2 , y₁ 2 ) i.e., O M=A M=B M Thus, aligned c=O M c & = x₁^2 2 + y₁^2 2 x₁^2+y₁^2 & =4 c^2 aligned Thus, locus is x^2+y^2=4 c^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