Find the standard form of the equation of the circle with endpoints of a diameter at the points and .
Type the standard form of the equation of this circle.
(Type an equation.)

Question

Find the standard form of the equation of the circle with endpoints of a diameter at the points $$ (3,6) $$ and $$ (-7,2) $$. Type the standard form of the equation of this circle. (Type an equation.)

UpStudy AI · Accepted Answer

Let the endpoints of the diameter be $$ A(3,6) $$ and $$ B(-7,2) $$.

1. **Find the center**:  
   The center $$ (h,k) $$ of the circle is the midpoint of $$\overline{AB}$$:
   $$
   h = \frac{3 + (-7)}{2} = \frac{-4}{2} = -2, \quad k = \frac{6+2}{2} = \frac{8}{2} = 4.
   $$
   So, the center is $$ (-2,4) $$.

2. **Find the radius**:  
   The distance between $$ A $$ and $$ B $$ is:
   $$
   d = \sqrt{(3 - (-7))^2 + (6-2)^2} = \sqrt{(10)^2 + (4)^2} = \sqrt{100+16} = \sqrt{116}.
   $$
   Since this is the diameter, the radius $$ r $$ is:
   $$
   r = \frac{\sqrt{116}}{2} = \sqrt{29}.
   $$

3. **Write the equation**:  
   The standard form of the circle with center $$ (-2, 4) $$ and radius $$ \sqrt{29} $$ is:
   $$
   (x+2)^2 + (y-4)^2 = 29.
   $$

$$ (x+2)^2 + (y-4)^2 = 29 $$
The standard form of the equation of the circle is $$ (x+2)^2 + (y-4)^2 = 29 $$.

Find the standard form of the equation of the circle with endpoints of a diameter at the points and .
Type the standard form of the equation of this circle.
(Type an equation.)

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Find the standard form of the equation of the circle with endpoints of a diameter at the points and . Type the standard form of the equation of this circle. (Type an equation.)

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Latest Geometry Questions

Find the standard form of the equation of the circle with endpoints of a diameter at the points and .
Type the standard form of the equation of this circle.
(Type an equation.)