Maximum number of parabolas that can be drawn with a given axis and tangent at vertex.
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 2 days ago
Blue
47.7k870151
asked 2 days ago
saket kumarsaket kumar
223
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saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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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 2 days ago
Blue
47.7k870151
asked 2 days ago
saket kumarsaket kumar
223
New contributor
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What do you mean by vertex?
– Todor Markov
2 days ago
Vertex of the parabola.
– saket kumar
2 days ago
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
– Todor Markov
2 days ago
That's means only 1 parabola is possible as per condition
– saket kumar
2 days ago
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
– Todor Markov
2 days ago
|
show 3 more comments
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 2 days ago
Blue
47.7k870151
asked 2 days ago
saket kumarsaket kumar
223
New contributor
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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 2 days ago
Blue
47.7k870151
asked 2 days ago
saket kumarsaket kumar
223
New contributor
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Blue
47.7k870151
asked 2 days ago
saket kumarsaket kumar
223
New contributor
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
Blue
47.7k870151
edited 2 days ago
Blue
47.7k870151
edited 2 days ago
Blue
47.7k870151
47.7k870151
asked 2 days ago
saket kumarsaket kumar
223
New contributor
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
saket kumarsaket kumar
223
asked 2 days ago
saket kumarsaket kumar
223
223
New contributor
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
saket kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What do you mean by vertex?
– Todor Markov
2 days ago
Vertex of the parabola.
– saket kumar
2 days ago
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
– Todor Markov
2 days ago
That's means only 1 parabola is possible as per condition
– saket kumar
2 days ago
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
– Todor Markov
2 days ago
|
show 3 more comments
What do you mean by vertex?
– Todor Markov
2 days ago
Vertex of the parabola.
– saket kumar
2 days ago
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
– Todor Markov
2 days ago
That's means only 1 parabola is possible as per condition
– saket kumar
2 days ago
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
– Todor Markov
2 days ago
What do you mean by vertex?
– Todor Markov
2 days ago
What do you mean by vertex?
– Todor Markov
2 days ago
Vertex of the parabola.
– saket kumar
2 days ago
Vertex of the parabola.
– saket kumar
2 days ago
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
– Todor Markov
2 days ago
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
– Todor Markov
2 days ago
That's means only 1 parabola is possible as per condition
– saket kumar
2 days ago
That's means only 1 parabola is possible as per condition
– saket kumar
2 days ago
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
– Todor Markov
2 days ago
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
– Todor Markov
2 days ago
|
show 3 more comments
1 Answer
1
active
oldest
votes
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 2 days ago
Todor MarkovTodor Markov
1,619410
add a comment |
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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 2 days ago
Todor MarkovTodor Markov
1,619410
add a comment |
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 2 days ago
Todor MarkovTodor Markov
1,619410
add a comment |
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 2 days ago
Todor MarkovTodor Markov
1,619410
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 2 days ago
Todor MarkovTodor Markov
1,619410
answered 2 days ago
Todor MarkovTodor Markov
1,619410
answered 2 days ago
Todor MarkovTodor Markov
1,619410
answered 2 days ago
Todor MarkovTodor Markov
1,619410
1,619410
add a comment |
add a comment |
saket kumar is a new contributor. Be nice, and check out our Code of Conduct.
saket kumar is a new contributor. Be nice, and check out our Code of Conduct.
saket kumar is a new contributor. Be nice, and check out our Code of Conduct.
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What do you mean by vertex?
– Todor Markov
2 days ago
Vertex of the parabola.
– saket kumar
2 days ago
If you know the axis, the tangent of the vertex is always perpendicular. Knowing it doesn't really give you anything new.
– Todor Markov
2 days ago
That's means only 1 parabola is possible as per condition
– saket kumar
2 days ago
No, you can make it as wide as you want, so infinitely many. You can also flip it upside down.
– Todor Markov
2 days ago