Write an equation for an ellipse centered at the origin, which has foci at (\pm\sqrt{12},0)(± 12 ,0)left parenthesis, plus minus, square root of, 12, end square root, comma, 0, right parenthesis and vertices at (\pm\sqrt{37},0)(± 37 ,0)left parenthesis, plus minus, square root of, 37, end square root, comma, 0, right parenthesis

Step-by-step explanation:

Given that :

the foci of the ellipse is (±√12,0) and C0-vertices are (0,±√37)

The foci are (-C,0) and (C ,0)

the focus has x-coordinates so the focus is  lie on x- axis.

The major axis also lie on x-axis

The minor axis lies on y-axis so C0-vertices are (0,±√37)

The given focus C = ae = √12

Given co-vertices ( minor axis) (0,±b) = (0,±√37)

b= √37

We can therefore express the  relation between the focus and semi major axes and semi minor axes as:

The equation of ellipse formula is:

and we know that

Thus ; the equation of the ellipse at the origin is

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where,

here given table is,

price ($), x   :           18         23       25       29       30       33

pairs sold, y :         16         13         10       8         6       2

so, ,   ,   ,

and   ,

thus, slop of the given line is,

⇒  

⇒   ≈ 33