Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202313 May 2023Evening ShiftMathematicsCircleActual

The abscissae of two points A and B are the roots of the equation x^2+2 a x-b^2=0 and their ordinates are roots of the equation y^2+2 p y- q ^2=0 . Then the equation of the circle with AB as diameter is given by

Options

  1. Ax^2+y^2-2 a x-2 p y+ ( b ^2+ q ^2 )=0
  2. Bx^2+y^2-2 a x-2 p y- ( b ^2+ q ^2 )=0
  3. Cx^2+y^2+2 a x+2 p y+ ( b ^2+ q ^2 )=0
  4. Dx^2+y^2+2 a x+2 p y- ( b ^2+ q ^2 )=0

Correct answer

D. x^2+y^2+2 a x+2 p y- ( b ^2+ q ^2 )=0

Step-by-step solution

Let A (x₁, y₁ ) and B (x₂, y₂ ) . According to the given condition, x₁+x₂=-2 a , x₁ x₂=- b ^2y₁+y₂=-2 p , y₁ y₂=- q ^2 The equation of the circle with A (x₁, y₁ ) and B (x₂, y₂ ) as the end points of diameter is (x-x₁ ) (x-x₂ )+ (y-y₁ ) (y-y₂ )=0 x^2+y^2-x (x₁+x₂ )-y (y₁+y₂ )+x₁ x₂+y₁ y₂=0 x^2+y^2+2 a x+2 p y- b ^2- q ^2=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