I'm having trouble with the following exercise and would like some help.
I need to find the intersection point of a curve and a normal to the curve knowining only the curve equation and a coordinate the normal passes by (which is not the intersection between the curve and the normal)
The curve equation is and the normal passes by the point
You've got a difficult problem there.
If you solve it analytically, you'll run into a third degree polynomial that does not have a neat solution.
Is it possible you are supposed to solve it using graphical methods?
Well there's a graph to illustrate the problem, but I'm not supposed to use it, no.
The exercice does have a star, which means it's a hard problem.
I suppose to teacher will explain it in class, but I had surgery and I'm gonna miss a couple weeks of school
One that would give you an approximation of the answer?
You have the 2 equations that Plato provided.
Do you know how to solve such a set of equations?
Basically you need to substitute the first in the second, that is, replace the occurrences of b in the second equation, by the b given by the first equation.
Arg sorry for being annoying, but the next question asks for the coordinate (7; 2) but when I try to solve using the above, I get 3 possible answers...? There's supposed to be 2 answers, but none of the 3 Given by wolframalpha are good :/
It would have a normal to the left, a symmetric normal to the right.... and a normal to the top!
Point is, you have an equation of the third degree.
It can have 1, 2, or 3 solutions.
In your case, 2 of the solutions are close together, near x=1.
ok, there can be more than one result if the point is inside the parabola.
But that's not the case here, if you look at the graph, you can see that the point (7, 2) is outside to the right, so I still don't get why there can be more than 2 intersections!
But anyway, I'm a complete fool. I misread. The point (7, 2) is touching a tangent, not a normal
It also applies outside the parabola - just not everywhere.
Usually there will be either 1 point or 3 points.
It will be rare if there are 2.
Aha! That explains it!But anyway, I'm a complete fool. I misread. The point (7, 2) is touching a tangent, not a normal