– WE ARE ASKED TO WRITE THE

CENTERED EQUATION OF A CIRCLE WITH A DIAMETER WITH END POINTS

(-2,1) AND (4,3). THE CENTERED EQUATION

OF A CIRCLE IS GIVEN HERE WHERE (H,K) ARE THE COORDINATES

OF THE CENTER, AND R IS THE LENGTH

OF THE RADIUS. SO KNOWING THE TWO ENDPOINTS

OF THE DIAMETER WHICH IS A SEGMENT THAT PASSES

THROUGH THE CENTER OF THE CIRCLE AND HAS TWO END POINTS

ON THE CIRCLE, WE WANT TO FIND THE CENTER

OF THE CIRCLE AND THE LENGTH OF THE RADIUS. TO UNDERSTAND

HOW TO APPROACH THIS, LET’S TAKE A LOOK AT THE CIRCLE

THAT HAS THESE TWO ENDPOINTS FOR A DIAMETER. HERE’S THE DIAMETER

WE WERE REFERRING TO. NOTICE HOW IT HAS ONE ENDPOINT

AT (-2,1), AND ANOTHER ENDPOINT AT (4,3). AGAIN, OUR GOAL HERE IS TO FIND

THE COORDINATES OF THE CENTER WHICH WOULD BE (H,K), AND THEN

THE LENGTH OF THE RADIUS WHICH WOULD BE THE LENGTH

OF THIS SEGMENT HERE. NOTICE HOW THE CENTER

OF THE CIRCLE WOULD BE THE MIDPOINT OF THE DIAMETER. AND THEN ONCE WE FIND

THE MIDPOINT OR THE CENTER OF THE CIRCLE, WE CAN THEN FIND

THE LENGTH OF THE RADIUS BY DETERMINING THE DISTANCE

FROM THE CENTER TO ONE OF THE TWO POINTS

ON THE CIRCLE. SO LET’S GO AHEAD AND DO THAT. AND, AGAIN, THE CENTER

WOULD HAVE COORDINATES (H,K) WHICH WOULD BE THE MIDPOINT

OF THE DIAMETER. THE MIDPOINT FORMULA

IS GIVEN HERE FOR REVIEW. WE’RE BASICALLY GOING TO FIND

THE AVERAGE OF THE X COORDINATES AND THE AVERAGE

OF THE Y COORDINATES. LET’S CALL THESE COORDINATES

THE 1s, X SUB 1 AND Y SUB 1. AND THESE COORDINATES THE 2,

X SUB 2, Y SUB 2. SO WE WOULD HAVE -2 + 4 DIVIDED

BY 2 AND 1 + 3 DIVIDED BY 2. WELL, -2 + 4=2. 2 DIVIDED BY 2 IS 1. AND 1 + 3=4. 4 DIVIDED BY 2 IS 2. SO NOW WE KNOW THAT

H=1 AND K=2. AND NOW TO FIND

THE LENGTH OF THE RADIUS WE’LL FIND THE DISTANCE

FROM THE CENTER TO ONE OF THE ENDPOINTS

OF THE DIAMETER. SO LET’S GO AHEAD

AND USE THE CENTER AND THIS FIRST ENDPOINT (-2,1). SO THE LENGTH OF THE RADIUS, OR

R, IS GOING TO BE EQUAL TO THE DISTANCE

BETWEEN THESE TWO POINTS AND THE DISTANCE FORMULA

IS GIVEN HERE. SO LET’S GO AHEAD

AND CALL THESE THE 1s, X SUB 1 AND Y SUB 1, AND THESE THE 2s,

X SUB 2, Y SUB 2. SO THE LENGTH OF THE RADIUS

OR THE DISTANCE IS GOING TO BE EQUAL

TO X SUB 2 – X SUB 1, OR -2 – 1 SQUARED + Y SUB 2 – Y

SUB 1 OR 1 – 2 SQUARED. SO WE’LL HAVE THE SQUARE ROOT

OF -3 SQUARED. THAT’S 9 PLUS (1 – 2)=-1. -1 SQUARED IS 1. SO THE RADIUS IS EQUAL

TO THE SQUARE ROOT 10. BUT FOR THE STANDARD EQUATION

OF THE CIRCLE WE NEED R SQUARED, NOT R. SO IF WE KNOW R EQUALS SQUARE

ROOT 10, WE CAN FIND R SQUARED BY SQUARING BOTH SIDES

OF THE EQUATION. AND THE SQUARE ROOT OF 10

SQUARED WOULD JUST BE 10. NOW THAT WE HAVE (H,K)

AND R SQUARED WE CAN WRITE THE EQUATION

IN STANDARD FORM. WE WOULD HAVE THE QUANTITY

X – H WHERE H IS 1. SO WE HAVE X – 1 SQUARED

+ (Y – K) WHERE K IS 2. SO WE HAVE Y – 2 SQUARED=R

SQUARED WHERE WE KNOW R=10. THIS WOULD BE THE STANDARD

EQUATION OF THE CIRCLE WITH THE DIAMETER

WITH THE GIVEN ENDPOINTS. I HOPE YOU FOUND

THIS EXPLANATION HELPFUL.

Thank you:)

Thanks a million

does it matter which endpoint you use? if I used (4,3) instead of (-2, 1) would it make a difference?

Thanks! That was really helpful!

Thankyouthankyouthankyou

your awesome thanks so much

Literally your amazing. explained this so well 🙂

Thank You!!! It was very helpful

This helped me understand the other parts. I thought you stop at the first part but i see now that there are more steps towards this. Thanks a bunch

Thank you for posting this video 🙂

great thankssssss

Thank you!

thank you so much for this video. it really made things clearer and easier to understand☺☺☺

This video really helped me! Very clear and easy to understand. Thank you very much for sharing.

Thanks a million times you saved me on my report today

XD you are my man..thx a lot…

Awesome! this also works for spheres if you add a third dimension of z. Thanks helped out in my Calculus 3 class..

Thank you thank you thank you thank you thank you. Keep making a lot of this… also make a programming tutorial with clear explaination like this thank you

tysm for this! x.

is this algebra 1 or 2

thank you!!! your video broke this down enough for the problem to make sense! take my thumbs up and subscription!