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 na madalas nakikita natin na lagay ng ice cream. So when we say conic sections, these are the curves that result from the intersection of a right circular cone and ng isang plane. Pero bago tayo pumunta din sa intersection ng ating cone and ng plane, discuss ko muna yung different parts ng ating right circular cone.
So, ang first part ng ating right circular cone is yung kanyang generator. Okay? So, ito yung kanyang slanting height.
So, tawagin na lang natin siyang generator. Then yung intersection ng dalawang generator is yan yung kanyang vertex. Okay?
Then kung magdadraw tayo guys ng vertical line na dadaan doon sa kanyang vertex, ito naman yung kanyang tinatawag na axis. Okay, so yan yung mga parts ng ating right circular cone. So punta na tayo ngayon dito sa cutting plane. And sa ating right circular cone. So again, conic section.
So these are the curves that result from the intersection ng cone and ng plane. So meaning, nakadepende yung ating curves. sa kung paano mag-intersect yung plane doon sa ating right circular cone. So, first, dito, makapansin nyo, yung ating cutting plane, okay, is parallel doon sa ating generator.
So kung gantong klase ikakat nung ating plane yung ating circular cone, yung curve na mabubuo natin dito is a parabola. Okay, so kung titignan nyo yung intersection nung ating plane at nung cone, makakapag-generate tayo dito klas ng parabola. Okay?
So next is yung sa may pangalawang figure natin. So as you notice, yung ating cutting plane is perpendicular naman siya doon sa ating axis. So again, yung axis is yung vertical line na dadaan doon sa vertex ng ating right circular cone.
So kung perpendicular... yung ating cutting plane doon sa right circular cone ang intersection na mabubuo natin dito is a circle kung titignan natin yung ating yung ating curve from the top ng top view tayo so ang mabubuo natin dito is a circle so So kung i-slant naman natin ng konti yung pag-cut ng ating plane sa ating right circular cone is mag-generate naman to guys ng ellipse. So medyo oval ang dating pag tinignan natin yung curve from the top sa top view ng ating cone.
So next naman is pag kinut naman natin yung ating... right circular cone vertically So, kung mapansin nyo na-intersect nung ating plane yung ating dalawang cones Okay? So, ang intersection na mabubuo ng ating plane at nung ating right circular cone is we have para siyang 2 parabolas Yun nga lang in our pre-calculus ang tawag natin dyan is hyperbola Okay? Okay.
Nakuha ba guys? So ito yung apat na curves na pag-aaralan natin dito sa ating pre-calculus class. So next is meron naman tayong tinatawag na degenerate conics. So ito yung mga iba pang lumabas na... Pwedeng point or pwedeng line na pwedeng ma-generate pag nag-intersect yung ating plane at yung right circular cone.
Yun nga lang, hindi na natin siya isasama sa ating conic section. So, nilimit lang natin sa apat, which is that yun yung ating mga circle, ellipse, parabola, and hyperbola. So ipapakita ko lang kung ano pa ba yung ibang lumabas pag nag-intersect yung plane and yung ating right circular cone. So dito guys, kung mapansin nyo, again, pag kinut ng ating...
yung right circular cone natin na perpendicular siya doon sa ating axis, makakapag-generate tayo ng circle. Yun nga lang, pag tumapat yung ating cutting plane, dun mismo sa vertex ng ating right circular cone, ang intersection nila is magiging point. Okay? Then, the same doon sa ating ellipse.
So kung yung kaating plane natin sa ellipse is tumapat dun sa vertex ng ating right circular cone, ang intersection ng ating plane at ng kaating right circular cone is magiging point 10. Okay? So next is dun sa parabola. So, alam naman natin yung cutting plane ng parabola is parallel doon sa ating isang generator. Okay? Then, if the cutting plane is sumacto mismo doon sa ating vertex, so, may intersect ng ating cutting plane yung ating isang generator.
Then, yung kanyang intersection is mag-create ng line. And last is yung sa ating hyperbola. If the vertical plane, guys, is tumapat dun mismo sa ating parang pinaka-axis, diba, na dumaan sa ating vertex, makakapag-create ito guys ng dalawang intersecting lines.
So, kumbaga, parang ang tatamahan niya is yung dalawang generator ng ating hyperbola. Okay? So, this is the end.
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!