Question

Identify the center and radius of the circle with the following equation: $\displaystyle(x+3)^2+(y+\frac{3}{2})^2=4$​

Answer 1

Answer:

Question : to identify the center and radius of the circle from the given equation

$\\ {(x + 3)}^{2} + (y + \frac{3}{2} {)}^{2} = 4$

This is the form of a circle. Use this form to determine the center and radius of the circle.

→

(x−h)²+(y−k)²=r²

Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

$= > \: \: \: \: \: r = 2 \\ = > \: h = - 3 \\ = > k = - \frac {3}{2}$

The center of the circle is found at (h,k).

Center: (−3,−3/2)

These values represent the important values for graphing and analyzing a circle.

Center:

$\\ \huge \: ( - 3 \: , \: \frac{ - 3}{2} )$

&

Radius: 2

Step-by-step explanation:

hope it's helpful,,

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Answer 2

Let's solve for x.

• $x+32+(y+32)2=4$

Step 1: Add -y^2 to both sides.

• $y^2+x+3y+45/4+−y^2=4−y^2x+3y+45/4=−y^2+4$

Step 2: Add -3y to both sides

• $=x+3y+45/4+−3y=−y^2+4−3yx+45/4=−y^2−3y+4$

Step 3: Add (-45)/4 to both sides.

• $x+45/4+−454=−y^2−3y+4+−45/4$
• $x=−y^2−3y+−294$

Answer:

• $x=−y^2−3y+ (−29/4)$