Question

: What are the coordinates of the center of the circle shown below?

Express your answer in the form (a,b) without using spaces.

X^2 + y^2 – 2x + 6y + 9 = 0

Answer: ________


: What is the radius of the circle shown below?

X^2 + y^2 – 12x – 6y + 9 = 0

Answer:_________

: What is the length of the major axis of the conic section shown below?

(x+2)^2 (y-1)^2
---------- + ---------- = 1
49 25


Answer:_______

Answer 1

Answer on Question #57354 - Math – Analytic Geometry

Question

1) What are the coordinates of the center of the circle shown below?

Express your answer in the form (a,b) without using spaces.

$$X ^ {\wedge} 2 + y ^ {\wedge} 2 - 2 x + 6 y + 9 = 0$$

Answer: __________

Solution

$$x ^ {2} + y ^ {2} - 2 x + 6 y + 9 = 0$$ $$x ^ {2} - 2 x + 1 + y ^ {2} + 6 y + 9 - 1 = 0$$ $$(x - 1) ^ {2} + (y + 3) ^ {2} = 1$$

Thus, the center is (1, -3).

**Answer**: (1, -3).

Question

2) What is the radius of the circle shown below?

$$X ^ {\wedge} 2 + y ^ {\wedge} 2 - 12x - 6y + 9 = 0$$

Answer: __________

Solution

$$x ^ {2} + y ^ {2} - 12x - 6y + 9 = 0$$ $$x ^ {2} - 12x + 36 + y ^ {2} - 6y + 9 - 36 = 0$$ $$(x - 6) ^ {2} + (y + 3) ^ {2} = 6 ^ {2}$$

Thus, the radius is 6.

**Answer:** 6.

Question

3) What is the length of the major axis of the conic section shown below?

$$\begin{array}{l} (x + 2)^2 \quad (y - 1)^2 \\ \hline x + 1 \\ \end{array} = 1$$

49 25

**Answer:** __________

Solution

$$\begin{array}{l} \frac{(x + 2)^2}{49} + \frac{(y - 1)^2}{25} = 1 \\ \frac{(x + 2)^2}{7^2} + \frac{(y - 1)^2}{5^2} = 1 \\ \Rightarrow \left\{ \begin{array}{l} a = 7 \\ b = 5 \end{array} \right. \\ \end{array}$$

Major axis: the longest diameter of an ellipse is $2a = 14$.

**Answer:** 14.

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