Complex Numbers<br><br><br><img src="https://tex.z-dn.net/?f=%5Cfrac%7B-1-2i%7D%7B-2%2Bi%7D" id="TexFormula1" title="\frac{-1-2i

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find

Evgesh-ka [11]

Answer:

The equation of the circle is $(x+3)^2+(y-5)^2 = 17$

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is the distance from the center to either endpoint of the diameter. Finally use the center-radius form to find the equation.

Find the center-radius form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

$(\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5)$ .

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by $\sqrt[]{(a-c)^2+(b-d)^2}$ . So, let us use (1,4) to calculate the radius.

$r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}$ .

REcall that given a point $(x_0,y_0)$ . The equation of a circle centered at the point $(x_0,y_0)$ is

$(x-x_0)^2+(y-y_0)^2 = r^2$

In our case, $(x_0,y_0)=(-3,5)$ and $r=\sqrt[]{17}$ . Then, the equation is

$(x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17$

4 0

2 years ago

Plz, help me I will give you a brainlist and Extra points. If you help me.

stiv31 [10]

Answer:

B) (4/9 x 20)-3

8 0

2 years ago

Please help and explain this

IRINA_888 [86]

Multiply each price by the discount into a decimal (move the decimal place over 2 on the percents) then subtract that from the regular price and that's sale price

3 0

3 years ago

Read 2 more answers

What is the slope of the line passing through the points

Bingel [31]

Hello!

Answer:

$\boxed{2}$

Step-by-step explanation:

$Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}$

$\frac{1-(-5)}{4-1}=\frac{6}{3}=2$

Therefore, the slope is 2, which is our final answer.

Hope this helps!

Have a nice day! :)

:D

Thank you!

6 0

3 years ago

on june 1, $40,000 of treasury bonds were purchased between interest dates. the broker commission was $600. the bonds pay intere

PtichkaEL [24]

Given:
treasury bond = 40,000
brokers commission = 600
interest rate = 12$ p.a
interest paid semi-annually, january 1 and july 1.

Since the treasury bond was sold on June 1, its interest revenue will only be equal to 1 month ( June 1 to July 1).

12% / 12 months = 1% per month

40,000 * 1% = 400 interest revenue to be recorded on July 1.

6 0

2 years ago