1.

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

Answer»

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


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