Question

Find the equation of the circle if end points of one of its diameters are (0, 1) and (-2,5).​

Answer 1

Answer:

x² + y² + 2x - 6y + 5 = 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+5)/2 )

                     = (-1 , 3)

Using distance formula,

Radius = distance b/w (-1, 3) and (0, 1)

            = √(-1 - 0)² + (3 - 1)²

            = √5

Thus, eq. of the circle is, if (x₁, y₁) is radius:

⇒ (x - x₁)² + (y - y₁)² = r²

⇒ (x - (-1))² + (y - 3)² = (√5)²

⇒ x² + 1 + 2x + y² + 9 - 6y = 5

⇒ x² + y² + 2x - 6y + 5 = 0

Answer 2

Answer:

Let A (0,1) ;B(-2,5)

(x-(0)) (x-1)+(y-(-2)) (y-5)=0

(x-0)(x-1)+(y+2)(y-5) =0

x square -x +y square -5y+2y-10=0

x square -x +y square -3y -10 =0

THEREFORE , the required equation is x square -x +y square -3y -10=0