Question

Determine the function which corresponds to the given graph. (3 points)

a natural logarithmic function crossing the x axis at negative two and y axis at one.


The asymptote is x = -3.

Answer 1

The center of the circle is c=50 and radius of the circle is
`r=√(3)`

Explanation:

Given circle equation is

`x^2-4x+y^2+14y=-50\hfill(1)`

Equation (1) can be written as
`x^2-4x+y^2+14y+50=0\hfill(2)`

we know that the equation of the circle is of the form

`x^2+y^2+2gx+2fy+c=0\hfill(3)`

with centre (-g,-f) and radius=
`√(g^2+f^2-c)`

when, g,f and c are constants

Now comparing the (2) and (3) equations we get 2g=-4

`g=(-4)/(2)`

`g=-2`

`2fy=14`

`f=(14)/(2)`

`f=7`

and
`c=50`

Now to find the centre and radius of the given circle equation, substituting the values of g,f,c in the formulae of centre and radius

centre=(-g,-f)

=(-(-2),-7)

centre=(2,7)

Radius=
`√(g^2+f^2-c)`

=
`√((-2)^2+(7)^2-50)`

=
`√(4+49-50)`

=
`53-50`

Radius=
`\srqt{3}`

The center of the circle is c=50 and the radius of the circle equation
`r=√(3)`