Homework problem (tangents equation)

In summary, the conversation is about finding the equations of tangents to a parabola and determining the surface/area formed by the parabola and tangents. The hint given is to use the slope of the line from the origin to a general point on the parabola to find the slope of the tangent.
  • #1
Penultimate
26
0
Could you help me solve this one :


Write the the equations of the tangents of the parabole x^2=2y-4 that go through the origin of coordinates. Whats the surface of the figure formed by the parabole and the tangents.

I am not sure i have translated thi one in an understanding way :(.
 
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  • #2
Hi Penultimate! :smile:

(try using the X2 tag just above the Reply box :wink:)
Penultimate said:
Write the the equations of the tangents of the parabola x2=2y-4 that go through the origin of coordinates.

Hint: the line from the origin to a general point P must have the same slope (gradient) as the tangent at P. :wink:
Whats the surface of the figure formed by the parabola and the tangents.

mmm … I don't understand that :confused: …

do you mean what's the area?
 

1. What is a tangents equation?

A tangents equation is a mathematical equation that describes the relationship between a line that touches a curve at a single point, known as the tangent, and the curve itself. It is used to find the slope of the tangent line at a specific point on the curve.

2. How do I solve a homework problem involving tangents equations?

To solve a homework problem involving tangents equations, you will need to identify the given information, such as the equation of the curve and the point of tangency. Then, you can use the formula for finding the slope of the tangent line, which is the derivative of the curve at the given point. Finally, plug in the values and solve for the slope or any other information that is being asked for in the problem.

3. What is the difference between a secant and a tangent line?

A secant line is a line that intersects a curve at two or more points, while a tangent line only touches the curve at one point. In other words, a secant line is a line that connects two points on a curve, while a tangent line is a line that touches the curve at a single point and has the same slope as the curve at that point.

4. How can I use tangents equations in real-life applications?

Tangents equations have many real-life applications, such as in physics, engineering, and architecture. They can be used to find the slope of a curved road or track, the direction of a moving object, or the angle of a building's roof. They are also used in calculus to find maximum and minimum values of a function, which is important in many fields of science and technology.

5. What are some common mistakes to avoid when working with tangents equations?

Some common mistakes to avoid when working with tangents equations include forgetting to find the derivative of the curve at the given point, using the wrong formula for finding the slope of the tangent line, and making calculation errors. It is also important to carefully read the problem and identify all the given information before starting to solve. Additionally, be sure to check your final answer to ensure it makes sense in the context of the problem.

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