Question

Find the equation of the circle if (2, -3) and (3, 1) are the extremities of the diameter.

Answer 1

Answer:

$\large\boxed{\sf{{x}^{2} + {y}^{2} - 5x + 2y + 3 = 0}}$

Step-by-step explanation:

Let's take an arbitrary point P(x,y) on the Circle.

Also, the diametric ends be A(x1,y1) and B(x2,y2).

The equation of the curcle is given by,

(x - x1)(x - x2) + (y - y1)(y - y2) = 0

Now, according to question, we have,

The end points of diameter are :-

• (2, -3)
• (3, 1)

Clearly, we have,

• x1 = 2
• x2 = 3
• y1 = -3
• y2 = 1

Therefore, the equation will be,

$= > (x - 2)(x - 3) + (y + 3)(y - 1) = 0 \\ \\ = > {x}^{2} - 3x - 2x + 6 + {y}^{2} - y + 3y - 3 = 0 \\ \\ = > {x}^{2} - 5x + 6 + {y}^{2} + 2y - 3 = 0 \\ \\ = > {x}^{2} + {y}^{2} - 5x + 2y + 3 = 0$

Hence, the required equation of circle is$\bold{{x}^{2} + {y}^{2} - 5 x + 2y +3 = 0}$