$$ 1 \leftarrow \quad $$ Give the center and radius in each of the following circles. $$ \quad \begin{array}{l} ext { a. } x^{2}+y^{2}=25 \ ext { b. }(x-9)^{2}+(y-3)^{2}=16 \ ext { c. }(x+7)^{2}+(y-2)^{2}=6 \ ext { d. } x^{2}+(y+5)^{2}=100 \ ext { a. The center is } \square ext {. } \ ext { (Type an ordered pair.) }\end{array} $$

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$$ 1 \leftarrow \quad $$ Give the center and radius in each of the following circles. $$ \quad \begin{array}{l}	ext { a. } x^{2}+y^{2}=25 \ 	ext { b. }(x-9)^{2}+(y-3)^{2}=16 \ 	ext { c. }(x+7)^{2}+(y-2)^{2}=6 \ 	ext { d. } x^{2}+(y+5)^{2}=100 \ 	ext { a. The center is } \square 	ext {. } \ 	ext { (Type an ordered pair.) }\end{array} $$

UpStudy AI · Accepted Answer

**a.**
- The equation is $$ x^2 + y^2 = 25 $$.  
- The standard form for a circle is $$ (x-h)^2 + (y-k)^2 = r^2 $$.  
- Here, $$ h=0 $$ and $$ k=0 $$, so the center is $$(0, 0)$$.  
- Since $$ r^2=25 $$, the radius is $$ r=\sqrt{25}=5 $$.

**b.**
- The equation is $$ (x-9)^2 + (y-3)^2 = 16 $$.  
- Comparing with the standard form $$ (x-h)^2 + (y-k)^2 = r^2 $$, we have $$ h=9 $$ and $$ k=3 $$, so the center is $$(9, 3)$$.  
- Since $$ r^2=16 $$, the radius is $$ r=\sqrt{16}=4 $$.

**c.**
- The equation is $$ (x+7)^2 + (y-2)^2 = 6 $$.  
- Rewrite $$ (x+7)^2 $$ as $$ (x-(-7))^2 $$. Thus, $$ h=-7 $$ and $$ k=2 $$, so the center is $$(-7, 2)$$.  
- Since $$ r^2=6 $$, the radius is $$ r=\sqrt{6} $$.

**d.**
- The equation is $$ x^2 + (y+5)^2 = 100 $$.  
- Rewrite $$ (y+5)^2 $$ as $$ (y-(-5))^2 $$. Thus, $$ h=0 $$ and $$ k=-5 $$, so the center is $$(0, -5)$$.  
- Since $$ r^2=100 $$, the radius is $$ r=\sqrt{100}=10 $$.
**a.** Center: $$(0, 0)$$, Radius: $$5$$ **b.** Center: $$(9, 3)$$, Radius: $$4$$ **c.** Center: $$(-7, 2)$$, Radius: $$\sqrt{6}$$ **d.** Center: $$(0, -5)$$, Radius: $$10$$

Give the center and radius in each of the following circles.

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