identify types of conic

Question

identify the which type of conic east of the following represents,

 

 

1.  (x-3)^2     +  (y-2)^2    = 1

        9                    4

 

2.  xy = 3

 

3.  (x + 1)^2     +  (y-2)^2  =  1

         25                   25

 

4.  (x+2)^2  +  (y-3)^2  = 49

 

 

5.  (x + 2)^2   -   (y -1)^2   = 1

        25                   9

 

 

6.  x^2 + 4x  = y - 4

Answer 1

First, the basic equations for conic sections are:

 

Circle
x² + y² = r²

 

 

Ellipse

x² / a² + y² / b² = 1

 

Parabola

4px = y²

 

 

Hyperbola

x² / a² - y² / b² = 1

 

Now, try and get these equations in standard form:

 

1.  Ellipse

2.  Rectangular hyperbola

3.  Circle

4.  Circle

5.  Hyperbola

6.  Parabola

 

*Hi L, sorry about #2, you were absolutely right, I did it incorrectly in my head.  But for #4, the reason why its a  circle and not a hyperbola is because it is in the standard form of a circle, i.e. (x - h)² + (y - k)² = r²

In that equation, h and k are the x and y coordinates of the center of the circle.  The equation I gave above for a circle assumes it is centered at the origin.