Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202123 Aug 2021Morning ShiftMathematicsCircleActual

If L₁ represents the radical axis of circles x^2+y^2-4 x-6 y+5=0 and x^2+y^2-2 x-4 y-1=0 and L₂ represents the radical axis of x^2+y^2+2 x+2 y-7=0 and x^2+y^2+x+y+9=0 , then

Options

  1. AL₁ is parallel to L₂ .
  2. BL₁ is perpendicular to L₂ .
  3. CL₁ and L₂ intersect at an angle 30^ .
  4. DL₁ and L₂ intersect at (1,7) .

Correct answer

A. L₁ is parallel to L₂ .

Step-by-step solution

Circles x^2+y^2-4 x-6 y+5=0 (S₁ ) and x^2+y^2-2 x-4 y-1=0 Equation of radical axis is aligned & S₁-S₂=0 & L₁: (x^2+y^2-4 x-6 y+5 )- & (x^2+y^2-2 x-4 y-1 )=0 aligned array ll & -2 x-2 y+6=0 & L₁: x+y-3=0 Similarly, & L₂: (x^2+y^2+2 x+2 y-7 )- & (x^2+y^2+x+y+9 )=0 & L₂: x+y-16=0 array From Eqs. (i) and (ii), we obtain m= coefficient of n coefficient of y m_ L₁ =m_ L₂ =-1 L₁ and L₂ are parallel.

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