# Math Help - when d1+d1=2a, ellipse. what is d1*d2=a^2?

1. ## when d1+d1=2a, ellipse. what is d1*d2=a^2?

ok so i was extremely bored in calculus class, and with my previous knowledge of how people made the ellipse and hyperbola equations... i tried to make an equation for this "definition"... and i couldn't do it.

since my mathematical imagination is limited, i was wondering if anyone knows whether that condition is even possible?

lemme rummage through my trash, i think i have the equation i ended up with, with center (0,0), foci (c,0) and (-c,0), and points (x,y)...

starting with:
$
\sqrt{(x-c)^2 + y^2}\sqrt{(x+c)^2 + y^2}=a^2$

i ended up with:
$
a^4-y^4-x^4-c^4 = 2c^2x^2 + 2y^2x^2 + 2c^2y^2$

i couldn't isolate y, or even $y^2$, so i couldn't punch this into the calculator, so is this graphable?

2. Originally Posted by Skerven
ok so i was extremely bored in calculus class, and with my previous knowledge of how people made the ellipse and hyperbola equations... i tried to make an equation for this "definition"... and i couldn't do it.

since my mathematical imagination is limited, i was wondering if anyone knows whether that condition is even possible?

lemme rummage through my trash, i think i have the equation i ended up with, with center (0,0), foci (c,0) and (-c,0), and points (x,y)...

starting with:
$
\sqrt{(x-c)^2 + y^2}\sqrt{(x+c)^2 + y^2}=a^2$

i ended up with:
$
a^4-y^4-x^4-c^4 = 2c^2x^2 + 2y^2x^2 + 2c^2y^2$

i couldn't isolate y, or even $y^2$, so i couldn't punch this into the calculator, so is this graphable?
The curve you have discovered is a Cassini Oval. Read this: Cassini Ovals -- from Wolfram MathWorld