00:01
Just to give you a visual of what's happening is we have y equals x squared minus 2.
00:05
So this is a parabola that looks like this.
00:10
And then we have a circle that is x squared plus y squared equals 8, which is a – oh, i should probably make this a little bit wider or longer.
00:27
Because what's happening is this is a circle whose radius is the square root of 8 which is a little bit smaller than 3 i'll type in the square root of 8 2 .828 so that's why i had to make this a little bit bigger because where the points are that we're looking at are actually up here so a is the vertex vertex.
00:59
B is here and c is here, and we're looking for the area of this triangle.
01:06
So what i need to do is, first of all, take this red equation.
01:11
I'm going to rewrite as 8 minus y squared, so i can substitute in this top equation.
01:16
So y will equal substituting x squared with 8 minus y squared, and that minus 2 is still there.
01:25
So i'm going to add the y squared to the left side plus y and 8 minus 2 is 6 so i'm going to subtract 6 to the left side and what do i get um y plus 3 y minus 2 and so we'll get answers of negative 3 and positive 2 for our solutions for y so i'm just thinking about what does x have have to be then well if y equals 2 let's do that one first then we all have 2 equals x squared minus 2 so if i add 2 over i'll get 4 equals x squared and x will equal positive or negative 2 and i'm pretty sure this negative 3 would be what i call extraneous because if i plug that in here when does negative 3 equal x squared minus 2 well if you add 2 over you'll get negative 1 and x squared cannot equal negative 1 so not gonna work for us so if i update my picture we have the vertices the b value being negative 2 i'm sorry i need to update my graph i don't know what i was thinking this graph actually looks like this and and then the circle is like this...