Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202415 May 2024Evening ShiftMathematicsCircleActual

If the sides of a rectangle are given by the equations x=-2, x=6, y=-2, y=5 , then the equation of the circle, drawn on the diagonal of this rectangle as its diameter, is

Options

  1. Ax^2+y^2+4 x+3 y+22=0
  2. Bx^2+y^2-4 x+3 y-22=0
  3. Cx^2+y^2-4 x-3 y-22=0
  4. Dx^2+y^2+4 x-3 y+22=0

Correct answer

C. x^2+y^2-4 x-3 y-22=0

Step-by-step solution

The given equations of the sides are x=-2, x=6, y=-2 and y=5 . Here, the diagonals AC and BD of rectangle ABCD are diameters of the circle passing through the vertices A , B , C and D . Considering diagonal AC with end points A(-2,-2) and C(6,5) , we get Equation of circle in diameter form as, aligned & (x-6)(x+2)+(y-5)(y+2)=0 & x^2-4 x-12+y^2-3 y-10=0 & x^2+y^2-4 x-3 y-22=0 aligned

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