Find the equation of the circle that has a diameter with endpoint located at (-5,-3) and (-11,-3).

Mathematics

1 answer:

GREYUIT [131]3 years ago

7 0

Check the picture below.

you can pretty much, without having to use the distance formula, see the diameter is 6 units long, thus the radius is half that or 3 then.

now, without having to use the midpoint formula, if we move from either endpoint inwards 3 units, we'll end up at the center, -5 -3, is just -8, so the center will be at -8, -3.

$\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
center~~(\stackrel{-8}{{{ h}}},\stackrel{-3}{{{ k}}})\qquad \qquad 
radius=\stackrel{3}{{{ r}}}
\\\\\\\
[x-(-8)]^2+[y-(-3)]^2=3^2\implies (x+8)^2+(y+3)^2=9$

You might be interested in

Jada solved the equation Negative StartFraction 4 over 9 EndFraction = StartFraction x over 108 EndFraction for x using the step

Lilit [14]

Answer: First option.

Step-by-step explanation:

The complete exercise is attached.

In order to solve this exercise, it is necessary to remember the following property:

The Multiplication property of Equality states that:

$If\ a=b\ then\ a*c=b*c$

In this case, the equation that Jada had is the folllowing:

$-\frac{4}{9}=\frac{x}{108}$

Jada needed to solve for the variable "x" in order to find its value.

The correct procedure to solve for for "x" is to multiply both sides of the equation by 108. Then, you get:

$(108)(-\frac{4}{9})=(\frac{x}{108})(108)\\\\-48=x$

As you can notice in the picture, Jada did not multiply both sides of the equation by 108, but multiplied the left side by $-\frac{4}{9}$ <em> </em>and the right side by $-\frac{9}{4}$ .