Question

Graph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). Label the center and at least four points on the circle. Write the equation of the circle.

Answer 1

@zpupster

Answer 2

@Zale101

Answer 3

helpp? please! will give metals!!

Answer 4

@johnweldon1993

Answer 5

What is the distance between these 2 points?

Answer 6

idk. it doesnt give me that.

Answer 7

...That's because you're supposed to find it...but we'll do that later...the general equation of a circle looks like

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

Thecenter of the circle is at point (h,k)

lets find that...it would be the midpoint between the 2 endpoints we were given

so use the fact that

\[\large Midpoint = (\frac{x_! + x_2}{2}),(\frac{y_1 + y_2}{2})\]

Plug in your 2 coordiantes into that equation and solve for the 'x' and the 'y' coordinates of the midpoint

Answer 8

(1,1)?

Answer 9

Correct...the center (or point (h,k) would be (1,1))

So now...back to our equation of a circle....

\[\large (x - 1)^2 + (y - 1)^2 = r^2\]

Now we want to solve for 'r' here....so pick one of your 2 points...

Answer 10

(-3,4)?

Answer 11

Okay...that (-3,4) will now be plugged in for 'x' and 'y' in that circle equation

\[\large (-3 - 1)^2 + (4 - 1)^2 = r^2\]
\[\large (-4)^2 + (3)^2 = r^2\]
\[\large 16 + 9 = r^2\]
\[\large 25 = r^2\]

Make sense how I simplified that?

So now...our original circle equation

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

will now look like

\[\large (x - 1)^2 + (y - k)^2 = 25\]

Answer 12

i think i get i, so when i graph it, the center point would be (-1,0)?

Answer 13

No the center point will be (1,1) like we found

Answer 14

oh ok.

Answer 15

so would the equation be (x-1)2+(y-1)2?

Answer 16

... = 25

Remember the whole equation is

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

so we need to include the founded r^2 = 25 in the equation..

\[\large (x - 1)^2 + (y - 1)^2 = 25\]

Answer 17

thank you!