Question

Find the equation of the circle which has the points (-2,3) and (0, -1) as opposite
ends of a diameter.​

Answer 1

Answer:

x² + y² + 2x - 2y - 3 = 0

Step-by-step explanation:

Mid point of the line joining them gives the radius of the circle.   Using mid-point formula,

Co. of radius = ((0+(-2))/2 , (-1+3)/2 )

                     = (-1 , 1)

Using distance formula,

Radius = distance b/w (-1, 1) and (0,-1)

            = √(-1 - 0)² + (1 - (-1))²

            = √5

Thus,  eq. of the circle is:

⇒ (x - x₁)² + (y - y₁)² = r²

⇒ (x - (-1))² + (y - 1)² = (√5)²

⇒ x² + 1 + 2x + y² + 1 - 2y = 5

⇒ x² + y² + 2x - 2y - 3 = 0

Answer 2

Step-by-step explanation:

If two ends of diameters are

 (x-x1)(x-x2)+(y-y1)(y-y2)=0

 (x+2)(x-3)+y(y+1)=0

x square -x-6+y square +y

REQUIRED EQUATION IS  x square +y square -x+y -6=0