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Wednesday, December 5, 2012

Determine whether an ellipse intersect a horizontal or vertical line

Assume an ellipse of width σ and length κσ is centered at (x0,y0), and has angle θ0 with the x-axis. How do we determine whether it intersects a horizontal line or a vertical line?

It turns out the criteria is very simple
  • The ellipse intersects a horizontal line y=y1 if and only if the following equation hods: 1=σ2(cos2(θ0)+κ2sin2(θ0))(y1y0)20
  • The ellipse intersects a vertical line x=x1 if and only if the following equation hods: 2=σ2(sin2(θ0)+κ2cos2(θ0))(x1x0)20

2 comments:

albert said...

hi i have a hard question if you help me i will be very happy; In a country, there are four types of banknotes: 5, 10, 20 and 25 unit values. Each banknote has a serial number with more than four digits. A banknote is chosen randomly. What is the probability that the sum of the four last digits of the serial number is bigger than the banknote unit value?

Note:Four banknote types, and all the serial numbers (...0000 - ...9999) can be chosen with equal probability.

Rum Tan said...

If the larger number is under the x, then the ellipse is horizontal. If it is under the y then it is vertical.

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