Homework problem (tangents equation)

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SUMMARY

The discussion centers on finding the equations of the tangents to the parabola defined by the equation x² = 2y - 4 that pass through the origin (0,0). Participants emphasize that the slope of the line from the origin to a point on the parabola must match the slope of the tangent at that point. Additionally, the conversation touches on determining the surface area of the figure formed by the parabola and its tangents, clarifying that the term "surface" refers to the area enclosed by these lines.

PREREQUISITES
  • Understanding of parabolic equations and their properties
  • Knowledge of calculus, specifically derivatives for finding slopes
  • Familiarity with coordinate geometry and tangent lines
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of tangent lines to parabolas
  • Learn how to calculate the area between curves using integration
  • Explore the concept of slopes in coordinate geometry
  • Investigate the properties of conic sections, particularly parabolas
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in understanding the geometric properties of parabolas and their tangents.

Penultimate
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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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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?
 

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