A circle is drawn on a coordinate plane with the center point at (4, −5) and a radius of 7.

Question

Derive the equation of the circle in standard form, using the given information and the Pythagorean theorem.

(1 point)
Responses

(x−4)2+(y+5)2=49open paren x minus 4 close paren squared plus open paren y plus 5 close paren squared is equal to 49

(x+4)2+(y−5)2=49open paren x plus 4 close paren squared plus open paren y minus 5 close paren squared is equal to 49

(x−4)2+(y+5)2=7open paren x minus 4 close paren squared plus open paren y plus 5 close paren squared is equal to 7

(x+4)2+(y+5)2=49open paren x plus 4 close paren squared plus open paren y plus 5 close paren squared is equal to 49

Answer 1

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

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

In this case, the center of the circle is \((4, -5)\) (so \(h = 4\) and \(k = -5\)), and the radius is \(7\).

First, calculate \(r^2\):

\[ r^2 = 7^2 = 49 \]

Now substitute the values of \(h\), \(k\), and \(r^2\) into the standard form equation:

\[ (x - 4)^2 + (y + 5)^2 = 49 \]

Thus, the correct equation of the circle in standard form is:

\[ (x - 4)^2 + (y + 5)^2 = 49 \]

So, the correct response is:

(x−4)²+(y+5)²=49