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일반적인 기하학 문제
f(x)(f(x))=x^2+1
f
(
x
)
(
f
(
x
)
)
=
x
2
+
1
y^2-2y-(x^2-x-1)=0
y
2
−
2
y
−
(
x
2
−
x
−
1
)
=
0
4x^2+4y^2-9+18y-9x^2=0
4
x
2
+
4
y
2
−
9
+
1
8
y
−
9
x
2
=
0
4x^2+16x-9y^2+18y=29
4
x
2
+
1
6
x
−
9
y
2
+
1
8
y
=
2
9
x^2-4x-2y^2=0
x
2
−
4
x
−
2
y
2
=
0
3y^2-x^2+18y-4x+20=0
3
y
2
−
x
2
+
1
8
y
−
4
x
+
2
0
=
0
9y^2-x^2=81
9
y
2
−
x
2
=
8
1
((y+2)^2)/(3^2)-((x-5)^2)/(5^2)=1
(
y
+
2
)
2
3
2
−
(
x
−
5
)
2
5
2
=
1
x^2-y^2+4x+16y-69=0
x
2
−
y
2
+
4
x
+
1
6
y
−
6
9
=
0
-(36(x-3)^2)/1+(25(y-4)^2)/1 =900
−
3
6
(
x
−
3
)
2
1
+
2
5
(
y
−
4
)
2
1
=
9
0
0
x^2-5y^2=3
x
2
−
5
y
2
=
3
((y+5)^2)/(100)-((x-4)^2)/(121)=1
(
y
+
5
)
2
1
0
0
−
(
x
−
4
)
2
1
2
1
=
1
10^2+x^2=y^2
1
0
2
+
x
2
=
y
2
8y^2-x^2-16y+8x-16=0
8
y
2
−
x
2
−
1
6
y
+
8
x
−
1
6
=
0
9x^2+36x-4y^2-16y-16=0
9
x
2
+
3
6
x
−
4
y
2
−
1
6
y
−
1
6
=
0
x^{(2)}-y^{(2)}=10(x-y)+1
x
(
2
)
−
y
(
2
)
=
1
0
(
x
−
y
)
+
1
(x^2)/(20^2)-(y^2)/(15^2)=1
x
2
2
0
2
−
y
2
1
5
2
=
1
7y^2-14x^2=98
7
y
2
−
1
4
x
2
=
9
8
((x^2)/(36))-(y^2)/(25)=1
(
x
2
3
6
)
−
y
2
2
5
=
1
(y^2)/4-(x^2)/1 =1
y
2
4
−
x
2
1
=
1
-4x^2+5y^2+8x-30y+21=0
−
4
x
2
+
5
y
2
+
8
x
−
3
0
y
+
2
1
=
0
((x+4)^2)/4-((y-1)^2)/9 =1
(
x
+
4
)
2
4
−
(
y
−
1
)
2
9
=
1
16x^2-96x-25y^2+200y-656=0
1
6
x
2
−
9
6
x
−
2
5
y
2
+
2
0
0
y
−
6
5
6
=
0
y^2=x^2+17
y
2
=
x
2
+
1
7
y^2=x^2+13
y
2
=
x
2
+
1
3
y^2=x^2+14
y
2
=
x
2
+
1
4
((y+4)^2)/1-((x-2)^2)/4 =1
(
y
+
4
)
2
1
−
(
x
−
2
)
2
4
=
1
((y-13)^2)/9-((x-10)^2)/(49)=1
(
y
−
1
3
)
2
9
−
(
x
−
1
0
)
2
4
9
=
1
(x^2)/3-(y^2)/3 =1
x
2
3
−
y
2
3
=
1
y^2=x^2+2x
y
2
=
x
2
+
2
x
625y^2-400x^2=2500
6
2
5
y
2
−
4
0
0
x
2
=
2
5
0
0
y^2-y-x-3=x^2-x-y-1
y
2
−
y
−
x
−
3
=
x
2
−
x
−
y
−
1
(y+2)^2-x^2+y-9=0
(
y
+
2
)
2
−
x
2
+
y
−
9
=
0
9x^2-y^2-36x-6y+36=0
9
x
2
−
y
2
−
3
6
x
−
6
y
+
3
6
=
0
y^2-x^2-2x-3=0
y
2
−
x
2
−
2
x
−
3
=
0
yy=x^2-2x
yy
=
x
2
−
2
x
36x^2-64y^2-504x+768y-2844=0
3
6
x
2
−
6
4
y
2
−
5
0
4
x
+
7
6
8
y
−
2
8
4
4
=
0
4x^2-5y^2+8x-10y+19=0
4
x
2
−
5
y
2
+
8
x
−
1
0
y
+
1
9
=
0
16y^2-9x^2-112y+36x+124=0
1
6
y
2
−
9
x
2
−
1
1
2
y
+
3
6
x
+
1
2
4
=
0
((x-1)^2)/4-((y+2)^2)/4 =1
(
x
−
1
)
2
4
−
(
y
+
2
)
2
4
=
1
((x-6)^2)/(25)-(y+1)^2=1
(
x
−
6
)
2
2
5
−
(
y
+
1
)
2
=
1
((y-6)^2)/9-(x-6)^2=1
(
y
−
6
)
2
9
−
(
x
−
6
)
2
=
1
((x+2)^2}{16}-\frac{y^2)/9 =1
(
x
+
2
)
2
1
6
−
y
2
9
=
1
((x-2)^2}{16}-\frac{(y+3)^2)/1 =1
(
x
−
2
)
2
1
6
−
(
y
+
3
)
2
1
=
1
(-p/((2-q)))(-((p-1))/q)=-1
(
−
p
(
2
−
q
)
)
(
−
(
p
−
1
)
q
)
=
−
1
2x^2-2y^2-20x+8y+34=0
2
x
2
−
2
y
2
−
2
0
x
+
8
y
+
3
4
=
0
y^2-16x^2+64x-200=0
y
2
−
1
6
x
2
+
6
4
x
−
2
0
0
=
0
4x^2-5y^2-24y-16=0
4
x
2
−
5
y
2
−
2
4
y
−
1
6
=
0
-3x^2+y^2-12=0
−
3
x
2
+
y
2
−
1
2
=
0
y^2=4x^2+3x+2
y
2
=
4
x
2
+
3
x
+
2
(((y+1)^2)/((1)))-(((x+1)^2)/((1)))=1
(
(
y
+
1
)
2
(
1
)
)
−
(
(
x
+
1
)
2
(
1
)
)
=
1
(v^2)/2 =2s^2-0.02
v
2
2
=
2
s
2
−
0
.
0
2
4x^2-9y^2=144
4
x
2
−
9
y
2
=
1
4
4
x^2-3y^2-3x=4y+5
x
2
−
3
y
2
−
3
x
=
4
y
+
5
(x^2)/(16)-(y^2)/(75.9)=1
x
2
1
6
−
y
2
7
5
.
9
=
1
3x^2-2y^2-6x+7y+7=0
3
x
2
−
2
y
2
−
6
x
+
7
y
+
7
=
0
(x-(-2))^2-(y-(-5))^2=(12)^2
(
x
−
(
−
2
)
)
2
−
(
y
−
(
−
5
)
)
2
=
(
1
2
)
2
3-4x+x^2-y^2>= 0
3
−
4
x
+
x
2
−
y
2
≥
0
y^2-16x^2-8y-96x-144=0
y
2
−
1
6
x
2
−
8
y
−
9
6
x
−
1
4
4
=
0
-((x+2)^2)/4+5y^2=1
−
(
x
+
2
)
2
4
+
5
y
2
=
1
9x^2-4y^2-54x-40y-55=0
9
x
2
−
4
y
2
−
5
4
x
−
4
0
y
−
5
5
=
0
((x+2/3)^2)/(1/9)-(y^2)/(1/3)=1
(
x
+
2
3
)
2
1
9
−
y
2
1
3
=
1
((y-1)^2)/9-((x-3)^2)/(16)=1
(
y
−
1
)
2
9
−
(
x
−
3
)
2
1
6
=
1
((y-1)^2)/4-((x+3)^2)/9 =1
(
y
−
1
)
2
4
−
(
x
+
3
)
2
9
=
1
x+x^2=y^2-4
x
+
x
2
=
y
2
−
4
9x^2+36x-8y^2+64y=164
9
x
2
+
3
6
x
−
8
y
2
+
6
4
y
=
1
6
4
9x^2-16y^2+144x+32y+79=0
9
x
2
−
1
6
y
2
+
1
4
4
x
+
3
2
y
+
7
9
=
0
0=y^2-y-(x^2)/4+24
0
=
y
2
−
y
−
x
2
4
+
2
4
4x^2-9y^2-16x+36y+16=0
4
x
2
−
9
y
2
−
1
6
x
+
3
6
y
+
1
6
=
0
(x^2}{16}-\frac{y^2)/7 =1
x
2
1
6
−
y
2
7
=
1
(x^2)/(64)-(y^2)/(81)=1
x
2
6
4
−
y
2
8
1
=
1
(x^2-4x+4)-(y^2-6y+9)=9
(
x
2
−
4
x
+
4
)
−
(
y
2
−
6
y
+
9
)
=
9
a^2+150=b^2+9
a
2
+
1
5
0
=
b
2
+
9
3x^2-5y^2=7
3
x
2
−
5
y
2
=
7
((x-2)^2)/4-((y-1)^2)/5 =1
(
x
−
2
)
2
4
−
(
y
−
1
)
2
5
=
1
6x^{(2)}-5y^{(2)}+24x+20y-56=0
6
x
(
2
)
−
5
y
(
2
)
+
2
4
x
+
2
0
y
−
5
6
=
0
(x^2)/(49)-((y+2)^2)/(79)=1
x
2
4
9
−
(
y
+
2
)
2
7
9
=
1
-(x^2)/(144)+(y^2)/(25)=1
−
x
2
1
4
4
+
y
2
2
5
=
1
((x-4)^2)/(16)-((y+2)^2)/(25)=1
(
x
−
4
)
2
1
6
−
(
y
+
2
)
2
2
5
=
1
y^2=(4x^2)/9-9
y
2
=
4
x
2
9
−
9
((y-3)^2)/(49)-((x+1)^2)/(16)=1
(
y
−
3
)
2
4
9
−
(
x
+
1
)
2
1
6
=
1
((y-1/4)^2)/4-((x+3)^2)/9 =1
(
y
−
1
4
)
2
4
−
(
x
+
3
)
2
9
=
1
f(x)f(x)=(15x^3-3x^2-12x)/(3x)
f
(
x
)
f
(
x
)
=
1
5
x
3
−
3
x
2
−
1
2
x
3
x
(y^2)/(100)-(x^2)/(49)=1
y
2
1
0
0
−
x
2
4
9
=
1
(x^2)/(16)-(y^2)/(33)=1
x
2
1
6
−
y
2
3
3
=
1
6x^2-5y^2+12x-30y-9=0
6
x
2
−
5
y
2
+
1
2
x
−
3
0
y
−
9
=
0
18y^2-4x^2=1
1
8
y
2
−
4
x
2
=
1
11^2-x^2+y^2=9^2
1
1
2
−
x
2
+
y
2
=
9
2
9(x-3)^2-4(y-1)^2=-36
9
(
x
−
3
)
2
−
4
(
y
−
1
)
2
=
−
3
6
x^2-y^2-2x-2y-1=0
x
2
−
y
2
−
2
x
−
2
y
−
1
=
0
solvefor x,h(x)^2=13x^2-6x+1
solvefor
x
,
h
(
x
)
2
=
1
3
x
2
−
6
x
+
1
(8(x^2-1/4))/(9/2)-9y^2 9/2 =(9/2)/(9/2)
8
(
x
2
−
1
4
)
9
2
−
9
y
2
9
2
=
9
2
9
2
9x^2-y^2=144
9
x
2
−
y
2
=
1
4
4
((x+4)^2)/4-((y-5)^2)/(45)=1
(
x
+
4
)
2
4
−
(
y
−
5
)
2
4
5
=
1
(-x^2)/(36)+(y^2)/(16)=1
−
x
2
3
6
+
y
2
1
6
=
1
(a^2-4b^2-15)/pi =0
a
2
−
4
b
2
−
1
5
π
=
0
x^2-1y^2=13
x
2
−
1
y
2
=
1
3
-9x^2+36x+4y^2-24y=63
−
9
x
2
+
3
6
x
+
4
y
2
−
2
4
y
=
6
3
3x^2-4y^2+3-6x+16y-18=0
3
x
2
−
4
y
2
+
3
−
6
x
+
1
6
y
−
1
8
=
0
(y^2)/(625)-(x^2)/(2500)=1
y
2
6
2
5
−
x
2
2
5
0
0
=
1
1
..
175
176
177
178
179
..
204
