find-the-equation-of-the-circle-which-ends-one-of-the-diameters-of-two-points-p-1-2-3-and-p-2-4-5-

Question Number 69462 by mhmd last updated on 23/Sep/19

f i n d t h e e q u a t i o n o f t h e c i r c l e w h i c h e n d s o n e o f t h e d i a m e t e r s o f t w o p o i n t s p_{1} (- 2, 3) a n d p_{2} (4, 5)

Commented by mathmax by abdo last updated on 23/Sep/19

l e t m (x, y) m \in C \Leftrightarrow m {\vec{p}}_{1} . m {\vec{p}}_{2} = 0 \Rightarrow (\begin{matrix} - 2 - x \\ 3 - y \end{matrix}) . (\begin{matrix} 4 - x \\ 5 - y \end{matrix}) = 0 \Rightarrow

(- 2 - x) (4 - x) + (3 - y) (5 - y) = 0 \Rightarrow - 8 + 2 x - 4 x + x^{2}

+ 15 - 3 y - 5 y + y^{2} = 0 \Rightarrow x^{2} + y^{2} - 2 x - 8 y + 7 = 0 \Rightarrow

C : x^{2} + y^{2} - 2 x - 8 y + 7 = 0