Question

Think about the graphs of the equations in the following system. x2+ y2 = 2 y = 2x2 – 3 Which of the following describes the system? circle with its center at (0, 0) and a radius of mc001-1.jpg; parabola opening up with its vertex at (0, –3) circle with its center at (0, 0) and a radius of mc001-2.jpg; parabola opening up with its vertex at (0, 3) circle with its center at (0, 0) and a radius of 2; parabola opening up with its vertex at (0, –3) circle with its center at (0, 0) and a radius of 2; parabola opening up with its vertex at (0, 3)

Answer 1

Answer: A

Step-by-step explanation:

Answer 2

circle: x2+ y2 = 2  

parabola: y = 2x2 – 3

 

The standard form of equation of circle is:

( x – h )^2 + ( y – k )^2 = r^2

We are given the equation x^2 + y^2 = 2.

Where h and k are the x and y coordinates of the center. Basing on the standard equation, the center is at (0 , 0) and r = $\sqrt{2}$

 

The standard form of equation of parabola with the axis of symmetry parallel to the y-axis is:

(x - h)^2 = 4p (y - k)

Rearranging the given equation into this form:

x^2 = (½) y + 3/2

x^2 = ½ (y + 3)

Since 4p is positive value, therefore the parabola is opening up. The vertex is located at (0 , -3).

 

Answer: circle with its center at (0, 0) and a radius of $\sqrt{2}$; parabola opening up with its vertex at (0, –3)