conic questions

Question

1)  is xy = 3  a rectangular hyperbola?

 

2.  is x^2 + 4X = y - 4  a parobola?

 

 

Answer 1

1) Yes. 

xy = 3 is a rectangular hyperbola.

This hyperbola lies in first and third quadrant.

Its asymptotes are x-axis (y = 0) and y-axis (x = 0).

Center: (0,0)

Transverse axis of symmetry: y=x

Domain: set of all real numbers except x=0

Vertices: (sqrt(3), sqrt(3)) and (-sqrt(3), - sqrt(3))

 

2) This is the equation of a parabola.

Its equation in standard form is y = ax²+bx+c.

For this parabola, it is y= x²+4x+4 where a=1, b=4, and c=4

Since a=1 is positive, this parabola opens upwards

 

The equation can be written as y = (x+2)² = (x-(-2))² + 0

This is of the form y = a(x-h)²+k where (h,k) is the vertex of the parabola.

So vertex of this parabola is (-2, 0)