SAT · Math · Geometry and Trigonometry
Ecuación de la circunferencia, arcos, sectores y ángulos en radianes.
$x2+y2-6x=16$ → $(x-3)2+y2=25$ → centro $(3, 0)$, radio 5.
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
A circle has a circumference of $18\pi$ centimeters. What is the radius, in centimeters, of the circle?
Respuesta numérica (escribes el número).
Respuesta: 9
The circumference is $C=2\pi r$. So $2\pi r=18\pi$ and $r=9$ centimeters.
$18$ is the diameter, not the radius.
$$x2+y2+8x-2y=19$$
The given equation defines a circle in the $xy$-plane. What is the radius of the circle?
Respuesta correcta: C. $6$
Complete the square for each variable. $x2+8x$ becomes $(x+4)2-16$, and $y2-2y$ becomes $(y-1)2-1$. So $(x+4)2+(y-1)2=19+16+1=36$. The radius is $\sqrt{36}=6$.
$36$ is $r2$, not $r$. $\sqrt{19}$ ignores the constants added when completing the square, and $\sqrt{34}$ subtracts the $1$ instead of adding it.
In the $xy$-plane, the graph of $x2+6x+y2-4y=12$ is a circle. What is the radius of the circle?
Respuesta numérica (escribes el número).
Respuesta: 5
Complete the square for each variable: $x2+6x=(x+3)2-9$ and $y2-4y=(y-2)2-4$. The equation becomes $(x+3)2+(y-2)2-13=12$, so $(x+3)2+(y-2)2=25$. The radius is $\sqrt{25}=5$.