Compare to base formula of: (x - h)² + (y - k)² = r² (x + 2)² + (y - 3)² = 36 Therefor: h = -2 (or -h = 2) k = 3 (or -k = -3) r² = 36 (or r = 6, as you take the square root to get r)
actually you can memorise the general form of equation of circle (x2+y2+Dx+Ey+F=0) h= -D/2, k= -E/2, r= √ ( (D/2)^2 + (E/2)^2 - F ) e.g. x2+y2-6x+10y+18=0 (D=-6, E=10, F=18) coordinates of the circle (h,k) = (3, -5) radius r = 4
I'm noticing a _distinct _*_lack_* of "needed this for a class"... Any explanation as to why these are skipped in most programs? Are they just _that_ niche?
The numerator of the eccentricity of an ellipse is the distance between the foci. The circle is a special case of an ellipse, where the two foci coincide at one point, called the center. Therefore, the numerator equals zero.
Your initial definition on parabola immediately made me think: If you make the cone bigger and move the bases further away would not every parabola eventually become an ellipsis? Only later you mentioned e=1 and it became clear the the parabola is parallel to the side and will always cut through the base no matter how big the cone is. But you did not mention that.
hmm i'm not sure i understand what you mean! a parabola can never be an ellipse because an ellipse does not intersect the base of the cone. a parabola is not parallel to anything, only a circle is parallel to the base.
_“because an ellipse does not intersect the base of the cone.”_ - just make the cone small enough then ellipse does intersect the base of the cone. iE. when the diameter of the base is smaller then mayor axis of the ellipse. You implicitly assume a sufficiently large cone. _“ parabola is not parallel to anything,”_ The parabola must be parallel to the opposite side to cone. Consider an infinite large cone. The parabola would need to cut through that infinitely far away base as well. Found this picture as well: blogs.adelaide.edu.au/maths-learning/files/2016/07/lineatinf-8.png blogs.adelaide.edu.au/maths-learning/files/2016/07/lineatinf-9.png Note the middle cone in the 2nd picture.
What you're saying contradicts the definition of an ellipse. An ellipse cuts across the cone with the same certainty that a square has four sides. You can't make a shape that contradicts the definition of that shape, it won't be that shape. It's like you're trying to draw a three-sided square. It's a triangle. If the shape intersects the base of the cone, it's a parabola, by definition. Also, there is no such thing as an infinitely large cone. No shape can be both infinitely large and have defined dimensions, because edges are boundaries, and something that is infinite does not have boundaries. I think you're working a little too hard to undo basic logic on this one.
What you saying makes sense with a finite base but this model assumes two infinitely extending cones. The eccentricity is kinda like a measure of the angle between the base and the slope of the cone. 0 being parallel with the base and 1 parallel with the slope. If our cones extend infinitely, then the eccentricity tells us if our slicing plane will intersect our infinitely far away base, and consequently the conic shape we are working with You cannot move the base to make an ellipse into a parabola.
Thank you very much, professor!!
legit, idk why teachers in class cant explain the same way... math can make you smile at times, thanks to this guy.
Your explanations are explicit.I like your teaching strategies.This was confusing but you made it as easy as A,B,C.Thank you,Prof Dave.
dude it's crazy how brilliant and enlightening your explanations are
So happy I found this site - can't wait to try some of the other subjects.
Why didn't i find you earlier!!!!!!!
You’ve made it easier for me. I never understood it in class. Keep the flames high
Sir, you are the best. I have no words to thank you. Sir go forward. We are always with you to support you😘😘
Thanks professor ... 🤗🤗🤗
Thank you professor!💗
Thank you so much Sir..I don't know how to express my gratitude.
What the
Thank you so much prof.
Thank u😭😭😭😭😭
U are a blessing😭😭😭😭😭
Thanks professor
Thanks professor Dave, I wish I would find you early.
Go until 1:30
Great review!
Great teacher
0:34 national flag of Bangladesh 🇧🇩 😂😂
Does the flag of Bangladesh refer to the sun rising in the jungle?
It's really amazing and easy way to teaching.thank you sir love you sir.
Thanks!
بارك الله فيكم وجزاكم الله خير الجزاء
من العراق ؟
Your lessons are much easier to understand
6:06 what do u mean add numbers on the right highlighting 36 and getting r = 6 ??? where did the 6 come from??
Compare to base formula of:
(x - h)² + (y - k)² = r²
(x + 2)² + (y - 3)² = 36
Therefor:
h = -2 (or -h = 2)
k = 3 (or -k = -3)
r² = 36 (or r = 6, as you take the square root to get r)
❤
legend
Done this lesson.
Thankyou math jesus
Lol
4:39 What if there was no image of a graph and you're only stuck to a set of h and k? can you find the radius there and is that possible to answer?
Thanks sir
Is there any way to know the coordinates of centre and radius of circle from the other form of equation
nope you have to complete the square!
You could always get it from the standard second degree curve equation
Thnx professor
actually you can memorise the general form of equation of circle (x2+y2+Dx+Ey+F=0)
h= -D/2, k= -E/2, r= √ ( (D/2)^2 + (E/2)^2 - F )
e.g. x2+y2-6x+10y+18=0 (D=-6, E=10, F=18)
coordinates of the circle (h,k) = (3, -5)
radius r = 4
Thanks a lot
Can we compute the eccentricity of the conic sections????
how on earth does this video only have 14k views!! also why didnt i find you earlier!!
Omg thanks
I'm noticing a _distinct _*_lack_* of "needed this for a class"...
Any explanation as to why these are skipped in most programs? Are they just _that_ niche?
No most people learn this in algebra 2
@@ProfessorDaveExplains
Oh...
I suppose I just had a lower standard in highschool. 😅
All the better that I'm subscribed I guess!
PDE = PDE, so Prof. Dave Explains is a Partial Differential Equation
xD
which part show its inclination coefficient
where is that video???
How can show its focus in double napped cone if cross section in cone
why did I find this just now lol
e is a ratio how e is equal to zero for a circle
The numerator of the eccentricity of an ellipse is the distance between the foci. The circle is a special case of an ellipse, where the two foci coincide at one point, called the center. Therefore, the numerator equals zero.
Can I get some quasicrystal mathamatics with my methodology, kind sir..?
So you're seeking crystal methodology.
@@TheLethalDomain LMAOOOO
N. V. N. Prasad
Your initial definition on parabola immediately made me think: If you make the cone bigger and move the bases further away would not every parabola eventually become an ellipsis?
Only later you mentioned e=1 and it became clear the the parabola is parallel to the side and will always cut through the base no matter how big the cone is. But you did not mention that.
hmm i'm not sure i understand what you mean! a parabola can never be an ellipse because an ellipse does not intersect the base of the cone. a parabola is not parallel to anything, only a circle is parallel to the base.
_“because an ellipse does not intersect the base of the cone.”_ - just make the cone small enough then ellipse does intersect the base of the cone. iE. when the diameter of the base is smaller then mayor axis of the ellipse. You implicitly assume a sufficiently large cone.
_“ parabola is not parallel to anything,”_ The parabola must be parallel to the opposite side to cone. Consider an infinite large cone. The parabola would need to cut through that infinitely far away base as well.
Found this picture as well:
blogs.adelaide.edu.au/maths-learning/files/2016/07/lineatinf-8.png
blogs.adelaide.edu.au/maths-learning/files/2016/07/lineatinf-9.png
Note the middle cone in the 2nd picture.
What you're saying contradicts the definition of an ellipse. An ellipse cuts across the cone with the same certainty that a square has four sides. You can't make a shape that contradicts the definition of that shape, it won't be that shape. It's like you're trying to draw a three-sided square. It's a triangle. If the shape intersects the base of the cone, it's a parabola, by definition. Also, there is no such thing as an infinitely large cone. No shape can be both infinitely large and have defined dimensions, because edges are boundaries, and something that is infinite does not have boundaries. I think you're working a little too hard to undo basic logic on this one.
What you saying makes sense with a finite base but this model assumes two infinitely extending cones. The eccentricity is kinda like a measure of the angle between the base and the slope of the cone. 0 being parallel with the base and 1 parallel with the slope.
If our cones extend infinitely, then the eccentricity tells us if our slicing plane will intersect our infinitely far away base, and consequently the conic shape we are working with
You cannot move the base to make an ellipse into a parabola.
bro you are looking like jesus for math
The intro
Jo bhart ke ho vo like kare
can you be my teacher?
طلاب سادس
Thank you so much prof