Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2019Evening ShiftMathematicsCircleActual

The equation of the circle concentric with the circle x 2 + y 2 - 6 x - 4 y - 12 = 0 and touching

Options

  1. Ax 2 + y 2 - 6 x - 4 y + 4 = 0
  2. Bx 2 + y 2 - 6 x - 4 y + 9 = 0
  3. Cx 2 + y 2 - 6 x - 4 y - 4 = 0
  4. Dx 2 + y 2 - 6 x - 4 y - 9 = 0

Correct answer

A. x 2 + y 2 - 6 x - 4 y + 4 = 0

Step-by-step solution

Given equation a circle x 2 + y 2 - 6 x - 4 y - 12 = 0 …. (i) Centre of circle (i) is (3, 2) Equation of circle concentric with circle (i) and touching the Y-axis is x - 3 2 + y - 2 2 = 3 2 ⇒ x 2 + 9 - 6 x + y 2 + 4 - 4 y = 9 ⇒ x 2 + y 2 - 6 x - 4 y + 4 = 0

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 MHT CET PYQs