Question

A$(x_1,y_1)$ and B$(x_2,y_2)$ are the end-points of diameter of a circle. Find the equation of the circle.

• A. (x + x₁) (x + x₂) + (y + y₁) (y + y₂) = 0
• B. (x - x₁) (x - x₂) + (y + y₁) (y + y₂) = 0
• C. (x - x₁) (x - x₂) + (y - y₁) (y - y₂) = 0
• D. (x + x₁) (x + x₂) - (y + y₁) (y + y₂) = 0

Answer 1

The correct option is C

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

This is a standard result and we recommend you to remember this formula. We will also see how to derive it.

P(x,y) is a point on the circle .we know the angle $\angle APB={90}^{\circ }$

$\Rightarrow$ slope of PA $\times$ slope of PB=-1

$\Rightarrow \frac{y-y_1}{x-x_1}\times \frac{y-y_2}{x-x_2}=-1$

$\Rightarrow (y-y_1)(y-y_2)=-(x-x_1)(x-x_2)$

$\Rightarrow (x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$