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Q01 |
- Parametric equation : x = tan(t) and y = sec(t)
- Q02 | - Parametric equation : x = sec(t) and y = tan(t)
- Q03 | - Diagrams of unit circle and unit hyperbola
- Q02 | - Parametric equation : x = sec(t) and y = tan(t)
Q01. Parametric equation : x = tan(t) and y = sec(t)
Question 1 : Find coordiantes of the foci
- Change to standard form of hyperbola
- Since 1 + tan(t)^2 = sec(t)^2
- If x = tan(t) and y = sec(t)
- Then 1 + x^2 = y^2
- Hence x^2 - y^2 = -1
- This is a hyperbola with principal axis y = 0
- Focal length f = Sqr(a^2 + b^2)
- Center is at (0,0)
- Vertices are at (0, 1) and (0, -1)
- Foci are at (0, Sqr(2)) and (0, -Sqr(2))
- y = +x is the asymptote
- y = -x is the asymptote
- (x/a)^2 - (y/b)^2 = +1 with principal axis x = 0
- (x/a)^2 - (y/b)^2 = -1 with principal axis y = 0
- Focal length f = Sqr(a^2 + b^2)
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Q02. Parametric equation : x = sec(t) and y = tan(t)
Question 1 : Find coordiantes of the foci
- Change to standard form of hyperbola
- Since 1 + tan(t)^2 = sec(t)^2
- If x = sec(t) and y = tan(t)
- Then 1 + y^2 = x^2
- Hence x^2 - y^2 = +1
- This is a hyperbola with principal axis x = 0
- Focal length f = Sqr(a^2 + b^2)
- Center is at (0,0)
- Vertices are at (1, 0) and (-1, 0)
- Foci are at (Sqr(2), 0) and (-Sqr(2), 0)
- y = +x is the asymptote
- y = -x is the asymptote
- (x/a)^2 - (y/b)^2 = +1 with principal axis x = 0
- (x/a)^2 - (y/b)^2 = -1 with principal axis y = 0
- Focal length f = Sqr(a^2 + b^2)
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Q03 Diagrams of unit circle and hyperbola
- 1. Find the curve of x = tan(t) and y = sec(t)
- 2. Find the curve of x = cot(t) and y = csc(t)
- 3. Find the curve of x = sec(t) and y = tan(t)
- 4. Find the curve of x = csc(t) and y = cot(t)
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