find-the-equation-of-the-circle-whose-center-is-the-origin-and-touches-the-line-3x-4y-15-0-

Question Number 69460 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 o s e c e n t e r i s t h e o r i g i n a n d t o u c h e s t h e l i n e 3 x - 4 y - 15 = 0

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

e q u a t i o n o f c i r c l e i s x^{2} + y^{2} = r^{2} a n d r = d (0, D)

D : 3 x - 4 y - 15 = 0 \Rightarrow d (0, D) = \frac{∣ 3 \times 0 - 4 \times 0 - 15 ∣}{\sqrt{3^{2} + {(- 4)}^{2}}} = \frac{15}{5} = 3 = r \Rightarrow

C : x^{2} + y^{2} = 9