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)

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 =

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).

The equation represents a circle of radius and center (0,0), and the equation represents a parabola with vertex (0,-3) and it opens upward.

Given information:

The given equations are:

Let's talk about the equations one by one.

The first equation is .

The given equation represents a circle with its center at (0,0) and radius . The equation can also be represented as,

Now, the second equation is . It is the equation of a parabola.

The given equation can be written as,

So, the vertex of the parabola is (0,-3) and it opens upwards. The opening is upwards because the coefficients of x and y are positive and y is related to x squared.

Therefore, the equation represents a circle of radius and center (0,0), and the equation represents a parabola with vertex (0,-3) and it opens upward.

See the image attached.

For more details, refer to the link:

link

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step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get