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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)

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meerkat18

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 = [tex] \sqrt{2} [/tex]

 

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 [tex] \sqrt{2} [/tex]; parabola opening up with its vertex at (0, –3)
aksnkj

The equation [tex]x^2+ y^2 = 2[/tex] represents a circle of radius [tex]\sqrt 2[/tex] and center (0,0), and the equation [tex]y=2x^2-3[/tex] represents a parabola with vertex (0,-3) and it opens upward.

Given information:

The given equations are:

[tex]x^2+ y^2 = 2\\y = 2x^2 - 3[/tex]

Let's talk about the equations one by one.

The first equation is [tex]x^2+ y^2 = 2[/tex].

The given equation represents a circle with its center at (0,0) and radius [tex]\sqrt2[/tex]. The equation can also be represented as,

[tex]x^2+ y^2 = 2\\(x-0)^2+(y-0)^2=(\sqrt2)^2[/tex]

Now, the second equation is [tex]y=2x^2-3[/tex]. It is the equation of a parabola.

The given equation can be written as,

[tex]y=2x^2-3\\y-(-3)=2(x-0)^2[/tex]

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 [tex]x^2+ y^2 = 2[/tex] represents a circle of radius [tex]\sqrt 2[/tex] and center (0,0), and the equation [tex]y=2x^2-3[/tex] represents a parabola with vertex (0,-3) and it opens upward.

See the image attached.

For more details, refer to the link:

https://brainly.com/question/15136456

Ver imagen aksnkj