Q. 34

Question

Find (a) the center (h, k) and radius r of each circle; (b) graph each circle; (c) find the intercepts if any of the equation $3 x^{2} + 3 y^{2} - 12 y = 0$

Step-by-Step Solution

Verified

Answer

a) center (h ,k), and the radius of the given equation are (0,2) and 2.

b) graph of the given equation is given below

1Part (a) Step 1. Given information

Here given the equation of the circle is $3 x^{2} + 3 y^{2} - 12 y = 0$

We have to Find (a) the center (h, k) and radius r of each circle

2Part (a) Step 2. Rewriting the equation of a circle

Given equation here is $3 x^{2} + 3 y^{2} - 12 y = 0$

we can by giving the parenthesis $3 x^{2} + 3 y^{2} - 12 y = 0 (x^{2}) + (y^{2} - 4 y) = 0 d i v i d e b y 3 t o g e t e q u a t i o n i n s \tan d a r d f o r m$

3Part (a) step 3 . Find the center and radius of the given circle

First, we have to complete the square of each parenthesis we get ${(x)}^{2} + (y^{2} - 4 y + 4) = 4 \sin c e a n y n u m b e r a d d e d t o t h e l e f t s i d e a d d e d t o t h e r i g h t s i d e {(x - 0)}^{2} + {(y - 2)}^{2} = 2^{2} t h i s i s s \tan d a r d f o r m o f t h e e q u a t i o n w i t h c e n t e r a n d r a d i u s . h e n c e c e n t e r i s (0, - 2) a n d r a d i u s i s 2 .$