The equation of a circle is given in standard form. Complete parts a through $$ c $$ to follow the step by step process to sketch the $$ (x+1)^{2}+(y-4)^{2}=29 $$ a) Determine the center and radius of the circle. The center of the circle is (Type an ordered pair.)

Question

UpStudy AI · Accepted Answer

The center of the circle is $$(-1, 4)$$. To determine the center and radius of the circle given by the equation $$(x+1)^{2}+(y-4)^{2}=29$$, we can compare it to the standard form of a circle's equation, which is: $$ (x - h)^{2} + (y - k)^{2} = r^{2} $$ where $$(h, k)$$ is the center of the circle and $$r$$ is the radius. From the given equation $$(x+1)^{2}+(y-4)^{2}=29$$: 1. The term $$(x + 1)^{2}$$ can be rewritten as $$(x - (-1))^{2}$$, indicating that $$h = -1$$. 2. The term $$(y - 4)^{2}$$ indicates that $$k = 4$$. 3. The right side of the equation, $$29$$, represents $$r^{2}$$. Therefore, to find the radius $$r$$, we take the square root of $$29$$: $$ r = \sqrt{29} $$ Now we can summarize the center and radius: - The center of the circle is $$(-1, 4)$$. - The radius of the circle is $$\sqrt{29}$$. Thus, the answer for part a is: The center of the circle is $$(-1, 4)$$.

The equation of a circle is given in standard form. Complete parts a through \( c \) to follow the step by step process to sketch the \( (x+1)^{2}+(y-4)^{2}=29 \) a) Determine the center and radius of the circle. The center of the circle is (Type an ordered pair.)

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

The equation of a circle is given in standard form. Complete parts a through \( c \) to follow the step by step process to sketch the \( (x+1)^{2}+(y-4)^{2}=29 \) a) Determine the center and radius of the circle. The center of the circle is (Type an ordered pair.)

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Related Questions