Solve Shortest Distance Point (0,c) from Parabola y=x^2

In summary, the conversation is about finding the shortest distance between the point (0,c) and the parabola y=x^2, where c ranges from 0 to 5. The speaker has solved the problem and obtained the answer (c-0.25)^0.5, but is having trouble understanding the significance of the range 0<= c <= 5. Another person suggests that the solution only works for c> 1/4 and prompts the speaker to consider what happens for values of c less than 1/4.
  • #1
gaganpreetsingh
24
0
Hi I am stuck on this ques. although i have solved and got the ans but i am still facing a problem.
Find the shortest distance of the point (0,c) from the parabola y=x^2 where 0<= c <= 5
i got the ans right that is
(c-0.25)^0.5
but i have not been able to understand the use of the 0<= c <= 5
any help?
 
Physics news on Phys.org
  • #2
any help out there?
 
  • #3
Assuming that c> 1/4, I get that. However, notice that your solution makes no sense if c< 1/4! What is the nearest point on the parabola if c< 1/4? (Hint: check the endpoints of the interval of values for y.)
 

What is the equation for a parabola?

The equation for a parabola is y = ax^2 + bx + c, where a, b, and c are constants. The value of a determines the direction and shape of the parabola, while the values of b and c determine its position on the coordinate plane.

How do you find the shortest distance between a point and a parabola?

To find the shortest distance between a point (0,c) and a parabola y = x^2, you can use the formula d = |(c - b)^2 - 4ac| / √(a^2 + 1), where a = 1 and b = 0. This formula calculates the distance between the point and the closest point on the parabola based on its equation.

What is the significance of the shortest distance between a point and a parabola?

The shortest distance between a point and a parabola is important because it tells us the minimum distance between the point and the parabola. This can be useful in many real-world applications, such as determining the shortest distance between a moving object and a curved surface or finding the closest point on a parabolic reflector for optimal signal reception.

How does the value of c affect the shortest distance between a point and a parabola?

The value of c in the parabola equation y = x^2 + c affects the y-intercept of the parabola, which in turn affects the position of the parabola on the coordinate plane. This value is also used in the formula for calculating the shortest distance between a point and the parabola, as it represents the y-coordinate of the point.

Can the shortest distance between a point and a parabola be negative?

Yes, the shortest distance between a point and a parabola can be negative. This usually occurs when the point is located below the x-axis and the parabola opens upward. In this case, the shortest distance is measured as a negative value because it is below the x-axis on the coordinate plane.

Similar threads

  • Calculus and Beyond Homework Help
Replies
5
Views
481
  • Calculus and Beyond Homework Help
Replies
2
Views
439
  • Calculus and Beyond Homework Help
Replies
14
Views
2K
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus
Replies
10
Views
2K
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
14
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
Back
Top