Y plane and we know that the xy plane has the equation Z equals zero. Now, the next part of our problem, we're told that the sphere sphere intersects the X. And since our radius is 5, 5 squared is going to be 25. So we have X -4 squared plus y minus zero, which is just going to be y squared plus z minus a negative to which we can write Z plus two squared. And we can go ahead and start writing it out. And so I have as a reference written in green the general form for the equation of the sphere. So we are given the center point of a sphere and its radius and we want to find its equation. In this problem, we will cover the equation of a sphere. This comes out to be well, one upon route 11 Former -3 upon wrote 11 Former Vanna Paul Route 11. Once upon underwrote one scared plus minus three is scared last one scared. Upon under route one scared plus minus is scared Less. Phone, two into 4 -1 in 27 Equals and upon one into 3 -2-1, C minus two means L upon one equals I am upon -3 equals and a 4th 1. We will write, they show these elements and elephants. And for second plane to help plus three M Plus seven an equal. Then we can write equation of normal L plus M plus two and equals zero.

They show up line of intersection line off intersection. In the plane is given and we have to find that kind of line of intersection of given plane.

And then this one appear will be a negative four pi over three. Um, this one will be, uh, just pie or a negative time. This one right here will be a negative three pi over four. So this one right here will be a negative pi over 64 at this angle Here will be, um this angle here will be a negative seven pi over four. Um, so with all this in mind, we also want to look at the, um, coordinates where the angle is negative from zero to negative. Andi, it'll be at a one point a little over 1.4. And then lastly, we have 11 Okay, if choir here, it'll be at pi over four. This is clearly going to be two pi over 36 or 62 pi over three. So with all this in mind, we want to graph our next point. Andi, the angle measure more importantly, is, um, five pi over four. Repeating perhaps so living in one third. 11 point 11.25 We could say, um perhaps a little higher than that too. It's a £5 before, and the length is about 10. Okay, But how can we located right here? That is three pi over. So this one right here falls on the 11 pi over six line, so it's going to be 11 pi over six. We see that this line right here would be, um, pie five or five as the r value and pious the faded value.

So first, we're going to put in a negative 50 Yeah. Um, and we want to plug in or different point values. So for this, we can look at this polar coordinate graph.

Mathematica 11.3 plot sphere