circle is drawn on a coordinate plane with the center point at (−4,6)

Question

and a radius of 2. Derive the equation of the circle from the given information. Fill in the missing information in the following equation.(2 points)
(x−
)2+
(y−
)2=

Answer 1

The standard equation of a circle with center \((h, k)\) and radius \(r\) is given by:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

For the given circle, the center is at \((-4, 6)\) and the radius is \(2\).

Here, \(h = -4\), \(k = 6\), and \(r = 2\).

Now we can substitute these values into the standard equation:

1. Substitute for \(h\):

   • Include \(-4\) in the equation: \((x - (-4))\)

2. Substitute for \(k\):

   • Include \(6\) in the equation: \((y - 6)\)

3. Substitute for \(r\):

   • The radius \(r = 2\), therefore \(r^2 = 2^2 = 4\).

Putting these values together results in the equation of the circle:

\[ (x + 4)^2 + (y - 6)^2 = 4 \]

So, filling in the missing information in your provided equation format, we get:

\[ (x - (-4))^2 + (y - 6)^2 = 4 \]

Thus, the completed equations are:

\[ (x - (-4))^2 + (y - 6)^2 = 4 \]

This indicates:

• The first blank is \(-4\)
• The second blank is \(6\)
• The third blank is \(4\)