Conic Section: Ellipse (Pretest)

Which of the following equations define an ellipse with center at  $(0,\ 0)$  and with its major axis at the x -axis?

•  $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$  

•  $\frac{x^2}{b^2}-\frac{y^2}{a^2}=1$  

•  $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$  

•  $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$  

Tags

CCSS.HSG.GPE.A.1

Which of the following is the center and vertices of the ellipse:  $\frac{x^2}{49}+\frac{y^2}{4}=1$  ?

• center: (7, 0) ; vertices: (0, –2), (0, 2)
  

• center: (0, 0) ; vertices: (–2, 0), (2, 0)
  

• center: (0, 0) ;  vertices: (0, –7), (0, 7)
  

• center: (0, 0) ; vertices: (–7, 0), (7, 0)
  

Tags

CCSS.HSG.GPE.A.1

If an ellipse has its center at the origin and its endpoints in each axis are (8, 0), (-8, 0) and (0,6), (0,-6), which of the following represents its equation?

•  $\frac{x^2}{64}+\frac{y^2}{36}=1$  

•  $\frac{x^2}{36}+\frac{y^2}{64}=1$  

•  $\frac{x^2}{64}-\frac{y^2}{36}=1$  

•  $\frac{x^2}{36}+\frac{y^2}{64}=1$  

Which of the following describes an ellipse with its center at the origin, focus at $(0,4)$ and vertex at $(0,7)$ ?

•  $\frac{x^2}{49}+\frac{y^2}{33}=1$  

•  $\frac{x^2}{33}+\frac{y^2}{49}=1$  

•  $\frac{x^2}{49}-\frac{y^2}{33}=1$  

•  $\frac{x^2}{33}-\frac{y^2}{49}=1$  

Tags

CCSS.HSG.GPE.A.1

What is the standard form of the equation of the ellipse with its foci at (±4, 0) and a major axis of length 12?

•  $\frac{x^2}{20}-\frac{y^2}{36}=1$  

•  $\frac{x^2}{36}-\frac{y^2}{20}=1$  

•  $\frac{x^2}{20}+\frac{y^2}{36}=1$  

•  $\frac{x^2}{36}+\frac{y^2}{20}=1$  

Tags

CCSS.HSG.GPE.A.1

Which of the following equations shows the standard form of an ellipse whose major axis is vertical, with the center located at  $(h,k)$ ?

•  $\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1$  

•  $\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$  

•  $\frac{\left(x-h\right)^2}{b^2}+\frac{\left(y-k\right)^2}{a^2}=1$  

•  $\frac{\left(x-h\right)^2}{b^2}-\frac{\left(y-k\right)^2}{a^2}=1$  

Which of the following equations satisfy the given conditions: parallel to the x –axis, center at (2, 5), longer axis of length 12 and shorter axis of length 5?

•  $\frac{\left(x-5\right)^2}{25}+\frac{\left(y-2\right)^2}{36}=1$  

•  $\frac{\left(x-2\right)^2}{25}+\frac{\left(y-5\right)^2}{36}=1$  

•  $\frac{\left(x-5\right)^2}{36}+\frac{\left(y-2\right)^2}{25}=1$  

•  $\frac{\left(x-2\right)^2}{36}+\frac{\left(y-5\right)^2}{25}=1$  

What is the foci of the ellipse $\frac{\left(x+3\right)^2}{144}+\frac{\left(y+1\right)^2}{169}=1$ ?

• (3, 4), (3,6)
  

• (3, 4), (3,-6)

• (4, 3), (6, 3)
  

• (4, 3), (-6, 3)
  

Which of the following is the general form of the equation $\frac{\left(x-3\right)^2}{64}+\frac{\left(y+1\right)^2}{36}=1$ ?

•  $7x^2+16y^2+54x+35y+470=0$  
  

•  $6x^2-14y^2-45x-45y-162=0$  
  

•  $9x^2+16y^2-54x+32y-479=0$  
  

•  $24x^2-54y^2+87x-113y+136=0$  
  

What is the equation of the ellipse with center at  $(3,–2)$ , passing through the vertices:  $(–4,–2)$ , $(10,–2)$ and  co – vertices:  $(3,1)$ , and $(3,-5)$ ?

•  $\frac{\left(x-3\right)^2}{49}+\frac{\left(y+2\right)^2}{9}=1$  

•  $\frac{\left(x-3\right)^2}{9}+\frac{\left(y+2\right)^2}{49}=1$  

•  $\frac{\left(x-2\right)^2}{49}+\frac{\left(y+3\right)^2}{9}=1$  

•  $\frac{\left(x-2\right)^2}{9}+\frac{\left(y+3\right)^2}{49}=1$