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.
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 $\sqrt{25}=5$.
A circle in the $xy$-plane has the equation $x2+y2-8x+6y=11$. For what positive value of $k$ is the line $y=k$ tangent to the circle?
Respuesta correcta: A. $3$
Complete the square: $(x-4)2+(y+3)2=11+16+9=36$, so the center is $(4, -3)$ and the radius is 6. A horizontal line is tangent where it touches the top or bottom of the circle: $y=-3+6=3$ or $y=-3-6=-9$. The positive value is $k=3$.
6 is the radius, not a $y$-value. 9 is the distance from the $x$-axis to the bottom tangent line ($y=-9$), which is negative. 11 is the constant from the original equation.