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

Answer:

The center of the circle is c=50 and radius of the circle is $r=\sqrt{3}$

Step-by-step 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=$\sqrt{g^2+f^2-c}$

when, g,f and c are constants

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

                                                                          $g=\frac{-4}{2}$

                                                                          $g=-2$

                                                                          $2fy=14$

                                                                          $f=\frac{14}{2}$

                                                                          $f=7$

                                                                 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=$\sqrt{g^2+f^2-c}$

                              =$\sqrt{(-2)^2+(7)^2-50}$

                             =$\sqrt{4+49-50}$

                            =$53-50$

                   Radius=$\srqt{3}$

The center of the circle is c=50 and the radius of the circle equation $r=\sqrt{3}$