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Home » The sides of a rectangle are given by the equations x = – 2, x = 4, y = – 2 and y = 5. Find the equation of the circle drawn on the diagonal of this rectangle as its diameter.
The sides of a rectangle are given by the equations x = – 2, x = 4, y = – 2 and y = 5. Find the equation of the circle drawn on the diagonal of this rectangle as its diameter.
CBSE | Circles | Class 11 | Exercise 21A | Maths | RS Aggarwal
The sides of a rectangle are given by the equations x = – 2, x = 4, y = – 2 and y = 5. Find the equation of the circle drawn on the diagonal of this rectangle as its diameter.

Answer:

The intersection points in clockwise fashion are:( – 2, 5), (4, 5), (4, – 2), ( – 2, -2).

The equation of a circle passing through the coordinates of the end points of diameters is (x – x1) (x – x2) + (y – y1)(y – y2) = 0

Substituting the values:(x1, y1) = ( – 2, 5) & (x2, y2) = (4, – 2)

(x + 2)(x – 4) + (y – 5)(y + 2) = 0

x2 – 4x + 2x – 8 + y2 + 2y – 5y – 10 = 0

x2 + y2 – 2x – 3y – 18 = 0

 

 

 

 

 

 

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