Hello guys, welcome back to my channel. In this video, I will show you the different types of conic sections. So when we say conic, it is derived from the word cone.
It is a geometric figure guys that we often see when we put ice cream. So when we say conic sections, these are the curves that result from the intersection. of a right circular cone and of a plane.
But before we go to the intersection of our cone and of the plane, I'll discuss first the different parts of our right circular cone. So the first part of our right circular cone is its generator. So this is its slanting height.
So let's just call it... generator then intersection and the long generator is you know can young vertex okay then come with the retire guys now vertical line nada and on second young vertex at the Namanu can young in a dog na axis okay so you know my apart not ating right circular cone. So let's go now here to the cutting plane and to our right circular cone.
So again, conic section. So these are the curves that result from the intersection of the cone and the plane. So meaning, our curves are dependent. on how the plane will intersect with the right circular cone.
First, here, you will notice that our cutting plane is parallel to our generator. If our circular cone is cut like this, the curve that we will build here is a parabola. Okay?
So, if you look at the intersection of our plane and cone, we can generate a class of parabola. Okay? So, next is the second figure. So, as you notice, our cutting plane is perpendicular to our axis.
So again, the axis is the vertical line that goes to the vertex of our right circular cone. So if our cutting plane is perpendicular to the right circular cone, the intersection that we will build here is a circle. If we look at our curve from the top view, what we will build here is a circle.
So if we will slant it a little, the cut of our plane in our right circular cone will generate an ellipse. So, the curve from the top is slightly oval when we look at the cone. Next, when we connect the right circular cone vertically, you will notice that the two cones intersect.
Okay, so the intersection that will form our plane and our right circular cone is we have like two parabolas but in our pre-calculus, what we call that is hyperbola Okay Did you get it guys? So these are the four curves that we will study in our pre-calculus class. So next is, we have what we call degenerate conics. So these are the other ones that came out. It can be a point or a line that can be generated if our plane intersects with the right circular cone.
However, we will not include it in our conic section. So we just limit it to four, which is that in our circles, ellipse, parabola, and hyperbola. So I will just show what else came out.
when the plane and right circular cone intersect so here guys if you notice again when our plane is cut our right circular cone which is perpendicular to our axis we can generate a circle but when our cutting plane is straight right there in the vertex of our right circular cone their intersection will be a point. Okay? Then, the same with our ellipse.
So, if our cutting plane in the ellipse is facing the vertex of our right circular cone, the intersection of our plane and our right circular cone will also be a point. Okay? So next is in the parabola. So we know that the cutting plane of the parabola is parallel to our generator.
Okay? Then if the cutting plane is the same as our vertex, so our cutting plane will intersect our generator. Then, the intersection will create a... line and last is the one in our hyperbola if the vertical plane guys is right there in our axis right?
that goes to our vertex it can create two intersecting lines so it will hit the two generators ng ating hyperbola okay so this is the end of our video i hope may natutunan kayo if you have questions or clarifications kindly put them in the comment section below so thank you guys for watching this is prof d i'll catch you on the flip side bye