analytic gemoetry problem

[snakeyesxlaw]

#1) Let f(x)=(x^2 - 11 x + 5)/8. The graph of function g is created by

* stretching the graph vertically by a factor of 16,
* then shifting the graph of f down 33 units,
* and finally shifting the graph left 3 units .

Find the function g.

#2) Suppose the graph of f is given and g(x) = 0.38 (f(-x) - 0.9). Which transformations are made to the graph of f in order to obtain the graph of g?

Shift up B units.
Shift down B units.
Shift right A units.
Shift left A units.
There is no shifting of the graph of f.

Find the value(s) for A and/or B.

Stretch by a factor of C.
Shrink by a factor of C.
There is no stretching or shrinking of the graph of f.

Find the value for B.

Reflect in the x-axis.
Reflect in the y-axis.
There is no reflection of the graph of f.

#3) Find an equation for the ellipse that satifies the given conditions:

Length of major axis: 42
Foci on the x-axis.
Passes through the point ( 10.5 , 12 )

NOTE: Use x and y in your answer.

im guessing,

(x^2 / 21^2) + ( y^2 / b^2) = 1

any suggestions?

#4) An ellipse passes through the points (16, 0) and (8, 3) and is in standard postion. Assuming the equation of the ellipse is in the form (x^2)/(c^2) + (y^2)/(d^2) = 1, then find the values of c and d.

 

[soroban]

Hello, snakeyesxlaw!

Find an equation for the ellipse that satifies the given conditions.
. . Length of major axis: 42
. . Foci on the x-axis
. . Passes through the point ( 10.5 , 12 )

You were well on your way . . .

\(\displaystyle \text{The equation of the ellipse is: }\;\frac{x^2}{21^2} + \frac{y^2}{b^2} \:=\:1\)
. . and we must determine \(\displaystyle b.\)

\(\displaystyle \text{The equation becomes: }\;b^2x^2 + 441y^2 \:=\:441b^2\quad\Rightarrow\quad b^2 \:=\:\frac{441y^2}{441-x^2}\)

\(\displaystyle \text{Since the point }(10.5},\:12)\text{ is on the ellipse: }\:b^2 \;=\;\frac{441(12^2)}{441-10.5^2} \:=\:192\)


\(\displaystyle \text{Therefore, the equation is: }\:\frac{x^2}{441} + \frac{y^2}{192} \;=\;1\)

 

[Deleted member 4993]

#1) Let f(x)=(x^2 - 11 x + 5)/8. The graph of function g is created by

* stretching the graph vertically by a factor of 16,
* then shifting the graph of f down 33 units,
* and finally shifting the graph left 3 units .

Find the function g.

#2) Suppose the graph of f is given and g(x) = 0.38 (f(-x) - 0.9). Which transformations are made to the graph of f in order to obtain the graph of g?

Shift up B units.
Shift down B units.
Shift right A units.
Shift left A units.
There is no shifting of the graph of f.

Find the value(s) for A and/or B.

Stretch by a factor of C.
Shrink by a factor of C.
There is no stretching or shrinking of the graph of f.

Find the value for B.

Reflect in the x-axis.
Reflect in the y-axis.
There is no reflection of the graph of f.

#3) Find an equation for the ellipse that satifies the given conditions:

Length of major axis: 42
Foci on the x-axis.
Passes through the point ( 10.5 , 12 )

NOTE: Use x and y in your answer.

im guessing,http://freemathhelp.com/forum/posting.php?mode=quote&f=10&p=103613#
#FF0000

(x^2 / 21^2) + ( y^2 / b^2) = 1

any suggestions?

#4) An ellipse passes through the points (16, 0) and (8, 3) and is in standard postion. Assuming the equation of the ellipse is in the form (x^2)/(c^2) + (y^2)/(d^2) = 1, then find the values of c and d.

This is pretty straight forward - where are you stuck?