Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.
match each circle equation to its corresponding center and radius.
center = (3,-5) radius = 7 units; center = (-3,5) radius = 2 units; center = (3,5) radius = 4 units; center = (3,5) radius = 2 units; center = (3,-5) radius = 4 units; center = (-3,-5) radius = 4 units
$(x + 3)^2 + (y + 5)^2 = 16$
$(x - 3)^2 + (y + 5)^2 = 16$
$(x + 3)^2 + (y - 5)^2 = 4$
$(x - 3)^2 + (y - 5)^2 = 4$

Explanation:

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step 1: Analyze \((x + 3)^2 + (y + 5)^2 = 16\)

Rewrite as \((x - (-3))^2 + (y - (-5))^2 = 4^2\). So center is \((-3, -5)\) and radius \(r = 4\) units.

Step 2: Analyze \((x - 3)^2 + (y + 5)^2 = 16\)

Rewrite as \((x - 3)^2 + (y - (-5))^2 = 4^2\). So center is \((3, -5)\) and radius \(r = 4\) units.

Step 3: Analyze \((x + 3)^2 + (y - 5)^2 = 4\)

Rewrite as \((x - (-3))^2 + (y - 5)^2 = 2^2\). So center is \((-3, 5)\) and radius \(r = 2\) units.

Step 4: Analyze \((x - 3)^2 + (y - 5)^2 = 4\)

Rewrite as \((x - 3)^2 + (y - 5)^2 = 2^2\). So center is \((3, 5)\) and radius \(r = 2\) units.

Answer:

• \((x + 3)^2 + (y + 5)^2 = 16\) → center \(= (-3, -5)\), radius \(= 4\) units
• \((x - 3)^2 + (y + 5)^2 = 16\) → center \(= (3, -5)\), radius \(= 4\) units
• \((x + 3)^2 + (y - 5)^2 = 4\) → center \(= (-3, 5)\), radius \(= 2\) units
• \((x - 3)^2 + (y - 5)^2 = 4\) → center \(= (3, 5)\), radius \(= 2\) units