Conics word problem question

[realVikash]

Hi how do this question? Would it be a good idea to put the center at Q or one of the other points? Also how would I go about solving this?

 

[skeeter]

I would set the origin at the center of both ...

top half of circle ...

[MATH]y = \sqrt{r^2-x^2}[/math]
you are given [MATH]y[/MATH] and [MATH]r[/MATH], solve for the value of [MATH]x_P>0[/MATH]
top half of ellipse ...

[MATH]y = b\sqrt{1 - \frac{x^2}{a^2}}[/MATH]
you are given [MATH]y[/MATH], [MATH]a[/MATH], and [MATH]b[/MATH], solve for the value of [MATH]x_R>0[/MATH]
finding the horizontal distance should be straightforward

 

[realVikash]

I would set the origin at the center of both ...

top half of circle ...

[MATH]y = \sqrt{r^2-x^2}[/math]
you are given [MATH]y[/MATH] and [MATH]r[/MATH], solve for the value of [MATH]x_P>0[/MATH]
top half of ellipse ...

[MATH]y = b\sqrt{1 - \frac{x^2}{a^2}}[/MATH]
you are given [MATH]y[/MATH], [MATH]a[/MATH], and [MATH]b[/MATH], solve for the value of [MATH]x_R>0[/MATH]
finding the horizontal distance should be straightforward

Hi, I'm from NZ we use (x-x1)^2 and (y=y1)^2 in our general equations, so what do r represent, and in all our high schools we don't teach the 2 formulas you've given me. I also did what you said and don't understand how to continue. Thanks for the help.

 

[skeeter]

circle centered at the origin ...

[MATH]x^2+y^2 = r^2[/MATH], where [MATH]r[/MATH] is the circle’s radius

ellipse centered at the origin ...

[MATH]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/MATH], where [MATH]a[/MATH] is the ellipse’s semi-axis length along the x-axis and [MATH]b[/MATH] is the ellipse’s semi-axis length along the y-axis.