conics-stretching horizontally about the line x=0

[gymnastqueen]

A circle x[sup:2ei5fzcu]2[/sup:2ei5fzcu]+y[sup:2ei5fzcu]2[/sup:2ei5fzcu]-2x-3=0 is stretched horizpntally by a factor of 2 on the line x=0. what is the equation of the resulting ellipse in general form?
So far I have (x-1)[sup:2ei5fzcu]2[/sup:2ei5fzcu]+y[sup:2ei5fzcu]2[/sup:2ei5fzcu]=4 (standard form) and I know I have to translate the graph 1 unit left so it is centered on x=0, but how do i stretch this horizontally by a factor of 2?

 

[Deleted member 4993]

A circle x[sup:34t8gxwj]2[/sup:34t8gxwj]+y[sup:34t8gxwj]2[/sup:34t8gxwj]-2x-3=0 is stretched horizpntally by a factor of 2 on the line x=0. what is the equation of the resulting ellipse in general form?
So far I have (x-1)[sup:34t8gxwj]2[/sup:34t8gxwj]+y[sup:34t8gxwj]2[/sup:34t8gxwj]=4 (standard form) and I know I have to translate the graph 1 unit left so it is centered on x=0, but how do i stretch this horizontally by a factor of 2?

If it is stretched in the x-direction by factor of 2 - then what is the magnitude of its major axis?

what is the magnitude of its minor axis?

 

[gymnastqueen]

it's a unit circle... so it's major axis if it were stretched horizontally by a factor of 2 to form an ellipse would then be 4units long? but how do i incorporate this into the equation when writing it?

 

[tkhunny]

A more useful form for this exercise is the ellipse form.

Generally,

\(\displaystyle \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1\)

Then we have a unit circle (Ellipse with major and minor axis equal to 2):

\(\displaystyle \frac{x^{2}}{1^{2}} + \frac{y^{2}}{1^{2}} = 1\)

Convince yourself that the expression above is your Unit Circle.

This makes changing the horizontal major axis to 4 a snap.

\(\displaystyle \frac{x^{2}}{2^{2}} + \frac{y^{2}}{1^{2}} = 1\)

It's a little more intuitive if you think about changing the semi-major axis to 2.