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P1(6,9)
P2(7,8)
M= 8-97-6= -11
Y-K= M(X-H)
Y-9=-1/1 (X-6)
1Y -9= -1X + 6
1X + 1Y – 15 = 0
P1(6,16)
P2(9,10)
M=10-169-6=63
Y-K= M(X-H)
Y – 16= 6/3(X-6)
3Y – 48= 6X – 36
-6X + 3Y - 12= 0
P1(10,7)
M=3/4
Y - K=M(X-H)
Y – 7=3/4(X-10)
-3X + 4Y + 2=0

ECUACION DE LA CIRCUNFERECIA
PROCEDIMIENTO
1. SE NOS ENTREGARA UN PUNTO CORDENADO Y UN RADIO
2. SE UTILIZARA LAFORMULA(X-H) + Y-K2=R2
3. SE SUSTITUIRAN LOS DATOS DE LA FORMULA
4. SE ELEVAN CON LA FORMULA SIGUIENTE:EL CUADRADO DEL PRIMER TERMINO + EL DOBLE PRODUCTO DEL PRIMERO* EL SEGUNDO + EL CUADRADO DEL 3ER TERMINO
5. TENDREMOS HAORA EL CUADRADO DEL TRINOMIO PERFECTO
6. SE IGUALARA A O BUSCANDO EL RADIO Y ELEVANDO AL CUADRADO AL OTRO LADO DE LA IGUALDAD
7. SE RESUMIRAN LOS NUMEROS NATURALES8. HAORA YA TENEMOS LA ECUACION LA COMPROBAMOS Y LA GRAFICAMOS

PROBLEMA EJEMPLO

CENTRO (5,9) Y RADIO (12)
(X-H)2+ (Y-K)2= R2
(X-5)2+ (Y- 9)2=(12)2
X2-10 X+25+Y2-18Y+ 81=144
X2+Y2- 10X-18Y+25+81-144=0
X2+Y2- 10X-18Y-38=0
X2-10X+___+Y2-18Y+___=+38
X2-10X+25+Y2-18Y+81=144
(X-5)2+ (Y-9)2=144
(X-H)2+(Y-K)2=R2

CENTRO (3,8) Y RADIO (13)
(X-H)2+ (Y-K)2= R2
(X-3)2+ (Y- 8)2=(13)2
X2-6X+9+Y2-16Y+ 64=169
X2+Y2- 6X-16Y+9+64-169=0
X2+Y2- 10X-18Y-96=0
X2-6X+___+Y2-16Y+___=+96
X2-6X+9+Y2-16Y+64=13
(X-3)2+ (Y-8)2=13
(X-H)2+(Y-K)2=R2

* (5,12) R=14
(X-H)2+ (Y-K)2= R2
(X-5)2+ (Y- 12)2=(14)2
X2-10 X+25+Y2-24Y+ 144=196
X2+Y2- 10X-24Y+25+144-196=0
X2+Y2- 10X-24Y-27=0
X2-10X+___+Y2-24Y+___=+196
X2-10X+25+Y2-24Y+144=196-25-144
(X-5)2+ (Y-12)2=14
(X-H)2+(Y-K)2=R2

*(4,6) R=14
(X-H)2+ (Y-K)2= R2
(X-4)2+ (Y- 6)2=(18)2
X2-8 X+16+Y2-12Y+ 36=324
X2+Y2- 8X-12Y+16+36-324=0
X2+Y2- 8X-12Y-272=0
X2-8X+___+Y2-12Y+___=+272
X2-8X+16+Y2-12Y+36=272-16-36
(X-4)2+ (Y-6)2=18
(X-H)2+(Y-K)2=R2
* (10,8) R=10
(X-H)2+ (Y-K)2= R2
(X-10)2+ (Y- 8)2=(10)2
X2-20 X+100+Y2-16Y+ 64=100
X2+Y2- 20X-16Y+100+64-100=0
X2+Y2-20X-16Y+64=0
X2-20X+___+Y2-16Y+___=-64X2-20X+100+Y2-16Y+64=-64+64+100
(X-10)2+ (Y-8)2=100
(X-H)2+(Y-K)2=R2

* (5,7) R=13
(X-H)2+ (Y-K)2= R2
(X-5)2+ (Y- 7)2=(13)2
X2-10X+25+Y2-14Y+ 49=169
X2+Y2- 10X-14Y+25+49-169=0
X2+Y2- 10X-14Y-95=0
X2-10X+___+Y2-14Y+___=+95
X2-10X+25+Y2-14Y+49=95-45-35
(X-5)2+ (Y-7)2=25
(X-H)2+(Y-K)2=R2
* (2,2) R=14
(X-H)2+ (Y-K)2= 42
(X-2)2+ (Y- 2)2=(4)2
X2-4 X+4+Y2-4Y+ 4=16
X2+Y2- 4X-4Y+4+4-16=0X2+Y2- 4X-4Y-16=0
X2-4X+___+Y2-4Y+___=16
X2-4X+4+Y2-4Y+4=16
(X-2)2+ (Y-2)2=4
(X-H)2+(Y-K)2=R2

* (-6,-10) R=18
(X-H)2+ (Y-K)2= R2
(X+6)2+ (Y+10)2=(18)2
X2+12 X+36+Y2+20Y+ 100=324
X2+Y2+ 12X+20Y+100+36-324=0
X2+Y2+12X+20Y-324=0
X2+12X+___+Y2+20Y+___=+324
X2+8X+16+Y2+20Y+36=324-36-100
(X+6)2+ (Y+10)2=18
(X-H)2+(Y-K)2=R2

* (-9,-5) R=20
(X-H)2+ (Y-K)2= R2
(X+9)2+ (Y+5)2=(20)2X2+18X+81+Y2+10Y+ 25=400
X2+Y2+ 18X+10Y+81+25-400=0
X2+Y2+18X+10Y-294=0
X2+18X+___+Y2+10Y+___=+294
X2+18X+81+Y2+10Y+25=294-81-25
(X+9)2+ (Y+5)2=20
(X-H)2+(Y-K)2=R2

* (-6,-8) R=17
(X-H)2+ (Y-K)2= R2
(X+6)2+ (Y+8)2=(17)2
X2+12 X+36+Y2+16Y+ 64=17
X2+Y2+ 12X+16Y+36+64-17=0
X2+Y2+12X+16Y+83=0
X2+12X+___+Y2+16Y+___=-83
X2+8X+16+Y2+16Y+64=-83+36+64
(X+6)2+ (Y+8)2=17
(X-H)2+(Y-K)2=R2* (-4,-8) R=27
(X-H)2+ (Y-K)2= R2
(X+4)2+ (Y+8)2=(27)2
X2+8 X+16+Y2+16Y+ 64=27
X2+Y2+ 8X+16Y+16+64-27=0
X2+Y2+8X+16Y+53=0
X2+8X+___+Y2+16Y+___=-53
X2+8X+16+Y2+16Y+64=53-16-64
(X+4)2+ (Y+8)2=27
(X-H)2+(Y-K)2=R2

* (5,-5) R=3
(X-H)2+ (Y-K)2= R2
(X-5)2+ (Y+5)2=(3)2
X2-10 X+25+Y2+10Y+ 25=9
X2+Y2- 10X+20Y+25+25-9=0
X2+Y2+12X+20Y+41=0
X2-10X+___+Y2-10Y+___=-41X2-10X+25+Y2+10Y+25=-41+25+25
(X-5)2+ (Y+5)2=3
(X-H)2+(Y-K)2=R2
* (-12.3,-14.5) R=27
(X-H)2+ (Y-K)2= R2
(X+12.3)2+ (Y+14.5)2=(27)2
X2+24.6 X+151.29+Y2+29Y+ 210.25=27
X2+Y2+ 24.6X+29Y+151.29+210.25-27=0
X2+Y2+24.6X+29Y+334.54=0
X2+24.6X+___+Y2+29Y+___=+334.54
X2+24.6X+151.29+Y2+29Y+210.25=334.54-210.25-151.29
(X+12.3)2+ (Y+14.5)2=27
(X-H)2+(Y-K)2=R2

* (-9.4,7.8) R=19
(X-H)2+ (Y-K)2= R2...