Ex - Graph a circle in standard form

- WELCOME TO AN EXAMPLE ON HOW TO GRAPH A CIRCLE GIVEN IN STANDARD FORM. THE STANDARD FORM OF A CIRCLE IS GIVEN HERE. [ PENCIL SCRATCHING] - WHERE WE HAVE THE QUANTITY X - H SQUARED + THE QUANTITY Y - K SQUARED = R SQUARED. WHERE THE (X) COORDINATE OF THE CENTER OF THE CIRCLE IS (H) AND THE (Y) COORDINATE OF THE CENTER OF THE CIRCLE IS (K). AND THE RADIUS OF THE CIRCLE IS EQUAL TO (R) WHERE ON THE RIGHT SIDE OF THIS EQUATION WE HAVE R SQUARED. SO GOING BACK TO OUR EXAMPLE. THE CENTER OF THE CIRCLE... [ PENCIL SCRATCHING ] - BECAUSE WE HAVE THE QUANTITY X - 2 SQUARED THE (X) COORDINATE OF THE CENTER IS +2. AND BECAUSE WE HAVE THE QUANTITY Y + 3 SQUARED THE (Y) COORDINATE IS -3. SO NOTICE HOW THE SIGNS OF THESE COORDINATES ARE THE OPPOSITE OF WHAT WE SEE HERE. MEANING IF WE HAVE A -2 HERE THE COORDINATE IS +2 AND IF WE HAVE +3 HERE THE COORDINATE IS -3. THIS IS BECAUSE IN STANDARD FORM WE'RE SUPPOSED TO HAVE X - H AND Y - K. SO WHEN WE HAVE Y + 3 IF WE WANTED TO WE COULD WRITE THIS AS Y - -3. BUT I THINK IT'S EASIER JUST TO REMEMBER THAT THE SIGN WILL BE THE OPPOSITE OF WHAT WE SEE HERE. THEN LOOKING AT THE RIGHT SIDE OF THIS EQUATION WE CAN DETERMINE THE RADIUS. JUST BE CAREFUL BECAUSE THE RIGHT SIDE IS ACTUALLY R SQUARED. SO WE KNOW R SQUARED IS EQUAL TO 16. SO WE'LL TAKE THE PRINCIPAL SQUARE ROOT OR POSITIVE SQUARE ROOT OF BOTH SIDES AND SINCE 4 x 4 IS EQUAL TO 16, R = 4 WHICH MEANS THE RADIUS IS EQUAL TO 4 UNITS. SO NOW THAT WE HAVE THE CENTER AND WE HAVE THE RADIUS LET'S GO AHEAD AND GRAPH THE CIRCLE. SO FIRST PLOT THE CENTER WHICH HAS COORDINATES (2, -3,) WHICH WOULD BE HERE. AND, NOW, BECAUSE THE RADIUS IS 4 UNITS TO SKETCH THIS BY HAND I'M GOING TO GO AHEAD AND GO UP 4 UNITS, DOWN 4 UNITS, RIGHT 4 UNITS AND LEFT 4 UNITS TO FIND FOUR POINTS ON THE CIRCLE. SO IF I GO UP 4 UNITS THIS POINT WOULD BE ON THE CIRCLE BECAUSE THE RADIUS IS 4. I CAN ALSO GO DOWN 4 UNITS FROM THE CENTER, RIGHT 4 UNITS FROM THE CENTER AND LEFT 4 UNITS FROM THE CENTER. AND NOW I'LL TRY TO SKETCH A CIRCLE PASSING THROUGH THESE FOUR POINTS. WELL, THAT'S NOT THE BEST CIRCLE BUT HOPEFULLY YOU GET THE IDEA. EVERY POINT ON THIS CIRCLE IS 4 UNITS FROM THIS BLUE CENTER. I HOPE YOU FOUND THIS HELPFUL.