It looks like the solution's manual was suggesting that so long as and are nonzero, this is the equation for an ellipse. If then . So, the solutions manual really should have written where and . In other words, they are a different and .
I'm doing some exercises and I came across this one that starts requesting an implicit differentiation of the second derivative:
I've done a few of these implicit differentiation by now but what's confusing me about this one is that the first step of the solutions manual transforms the equation into:
Later of course the right side of the equation is set to 0 and x' and y' are calculated. This first step above though has me wondering how the first equation which is a product of x^2a^2 and y^2b^2 gets changed to a division of each respectively looks strange to me. I'm wondering if anyone may have a better understanding of how those might be equivalent?
Thanks in advance...
It looks like the solution's manual was suggesting that so long as and are nonzero, this is the equation for an ellipse. If then . So, the solutions manual really should have written where and . In other words, they are a different and .