Mixing
Maximum number of parabolas that can be drawn with a given axis and tangent at vertex.
$begingroup$
If the equation of axis and the tangent at vertex are given, then what is the maximum number of parabolas that can be drawn?
My approach is this: Since the equation of axis and tangent at the vertex is fixed, then only 1 parabola is possible. Am I right? Or are there infinitely-many parabolas that can drawn by the given condition?
conic-sections
edited Jan 5 at 17:21
Blue
47.9k870152
asked Jan 5 at 17:01
saket kumarsaket kumar
416
$endgroup$
|
show 3 more comments
$begingroup$
If the equation of axis and the tangent at vertex are given, then what is the maximum number of parabolas that can be drawn?
My approach is this: Since the equation of axis and tangent at the vertex is fixed, then only 1 parabola is possible. Am I right? Or are there infinitely-many parabolas that can drawn by the given condition?
conic-sections
edited Jan 5 at 17:21
Blue
47.9k870152
asked Jan 5 at 17:01
saket kumarsaket kumar
416
$endgroup$
$begingroup$
What do you mean by vertex?
$endgroup$
– Todor Markov
Jan 5 at 17:33
$begingroup$
Vertex of the parabola.
$endgroup$
– saket kumar
Jan 5 at 17:36
$begingroup$
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
$endgroup$
– Todor Markov
Jan 5 at 17:37
$begingroup$
That's means only 1 parabola is possible as per condition
$endgroup$
– saket kumar
Jan 5 at 17:39
$begingroup$
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
$endgroup$
– Todor Markov
Jan 5 at 17:39
|
show 3 more comments
$begingroup$
If the equation of axis and the tangent at vertex are given, then what is the maximum number of parabolas that can be drawn?
My approach is this: Since the equation of axis and tangent at the vertex is fixed, then only 1 parabola is possible. Am I right? Or are there infinitely-many parabolas that can drawn by the given condition?
conic-sections
edited Jan 5 at 17:21
Blue
47.9k870152
asked Jan 5 at 17:01
saket kumarsaket kumar
416
$endgroup$
If the equation of axis and the tangent at vertex are given, then what is the maximum number of parabolas that can be drawn?
My approach is this: Since the equation of axis and tangent at the vertex is fixed, then only 1 parabola is possible. Am I right? Or are there infinitely-many parabolas that can drawn by the given condition?
conic-sections
conic-sections
edited Jan 5 at 17:21
Blue
47.9k870152
asked Jan 5 at 17:01
saket kumarsaket kumar
416
edited Jan 5 at 17:21
Blue
47.9k870152
asked Jan 5 at 17:01
saket kumarsaket kumar
416
edited Jan 5 at 17:21
Blue
47.9k870152
edited Jan 5 at 17:21
Blue
47.9k870152
edited Jan 5 at 17:21
Blue
47.9k870152
47.9k870152
asked Jan 5 at 17:01
saket kumarsaket kumar
416
asked Jan 5 at 17:01
saket kumarsaket kumar
416
asked Jan 5 at 17:01
saket kumarsaket kumar
416
416
$begingroup$
What do you mean by vertex?
$endgroup$
– Todor Markov
Jan 5 at 17:33
$begingroup$
Vertex of the parabola.
$endgroup$
– saket kumar
Jan 5 at 17:36
$begingroup$
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
$endgroup$
– Todor Markov
Jan 5 at 17:37
$begingroup$
That's means only 1 parabola is possible as per condition
$endgroup$
– saket kumar
Jan 5 at 17:39
$begingroup$
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
$endgroup$
– Todor Markov
Jan 5 at 17:39
|
show 3 more comments
$begingroup$
What do you mean by vertex?
$endgroup$
– Todor Markov
Jan 5 at 17:33
$begingroup$
Vertex of the parabola.
$endgroup$
– saket kumar
Jan 5 at 17:36
$begingroup$
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
$endgroup$
– Todor Markov
Jan 5 at 17:37
$begingroup$
That's means only 1 parabola is possible as per condition
$endgroup$
– saket kumar
Jan 5 at 17:39
$begingroup$
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
$endgroup$
– Todor Markov
Jan 5 at 17:39
$begingroup$
What do you mean by vertex?
$endgroup$
– Todor Markov
Jan 5 at 17:33
$begingroup$
What do you mean by vertex?
$endgroup$
– Todor Markov
Jan 5 at 17:33
$begingroup$
Vertex of the parabola.
$endgroup$
– saket kumar
Jan 5 at 17:36
$begingroup$
Vertex of the parabola.
$endgroup$
– saket kumar
Jan 5 at 17:36
$begingroup$
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
$endgroup$
– Todor Markov
Jan 5 at 17:37
$begingroup$
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
$endgroup$
– Todor Markov
Jan 5 at 17:37
$begingroup$
That's means only 1 parabola is possible as per condition
$endgroup$
– saket kumar
Jan 5 at 17:39
$begingroup$
That's means only 1 parabola is possible as per condition
$endgroup$
– saket kumar
Jan 5 at 17:39
$begingroup$
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
$endgroup$
– Todor Markov
Jan 5 at 17:39
$begingroup$
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
$endgroup$
– Todor Markov
Jan 5 at 17:39
|
show 3 more comments
1 Answer
1
active
oldest
votes
$begingroup$
The tangent at the vertex is always perpendicular to the axis. So, if you know the axis and the tangent at the vertex, it's essentially the same as knowing the axis and the vertex only. So you can make your parabola arbitrarily wide, and you can also flip it, so essentially you have infinitely many parabolas.
If, instead, you have the axis, a point not on the axis (i.e. not the vertex), and a tangent to that point, then in general you'd have a unique parabola.
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
$endgroup$
add a comment |
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1 Answer
1
active
oldest
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1 Answer
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active
oldest
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$begingroup$
The tangent at the vertex is always perpendicular to the axis. So, if you know the axis and the tangent at the vertex, it's essentially the same as knowing the axis and the vertex only. So you can make your parabola arbitrarily wide, and you can also flip it, so essentially you have infinitely many parabolas.
If, instead, you have the axis, a point not on the axis (i.e. not the vertex), and a tangent to that point, then in general you'd have a unique parabola.
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
$endgroup$
add a comment |
$begingroup$
The tangent at the vertex is always perpendicular to the axis. So, if you know the axis and the tangent at the vertex, it's essentially the same as knowing the axis and the vertex only. So you can make your parabola arbitrarily wide, and you can also flip it, so essentially you have infinitely many parabolas.
If, instead, you have the axis, a point not on the axis (i.e. not the vertex), and a tangent to that point, then in general you'd have a unique parabola.
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
$endgroup$
add a comment |
$begingroup$
The tangent at the vertex is always perpendicular to the axis. So, if you know the axis and the tangent at the vertex, it's essentially the same as knowing the axis and the vertex only. So you can make your parabola arbitrarily wide, and you can also flip it, so essentially you have infinitely many parabolas.
If, instead, you have the axis, a point not on the axis (i.e. not the vertex), and a tangent to that point, then in general you'd have a unique parabola.
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
$endgroup$
The tangent at the vertex is always perpendicular to the axis. So, if you know the axis and the tangent at the vertex, it's essentially the same as knowing the axis and the vertex only. So you can make your parabola arbitrarily wide, and you can also flip it, so essentially you have infinitely many parabolas.
If, instead, you have the axis, a point not on the axis (i.e. not the vertex), and a tangent to that point, then in general you'd have a unique parabola.
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
answered Jan 5 at 17:48
Todor MarkovTodor Markov
1,854410
1,854410
add a comment |
add a comment |
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$begingroup$
What do you mean by vertex?
$endgroup$
– Todor Markov
Jan 5 at 17:33
$begingroup$
Vertex of the parabola.
$endgroup$
– saket kumar
Jan 5 at 17:36
$begingroup$
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
$endgroup$
– Todor Markov
Jan 5 at 17:37
$begingroup$
That's means only 1 parabola is possible as per condition
$endgroup$
– saket kumar
Jan 5 at 17:39
$begingroup$
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
$endgroup$
– Todor Markov
Jan 5 at 17:39