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Q01 |
- Diagram : Parabola R = D/(1 - cos(A))
- Q02 | - Compare R = D/(1 - sin(A)) with R = D/(1 - cos(A))
- Q03 | - Compare R = D/(1 - sin(A)) and y = (x^2)/(2*D) - D/2
- Q04 | - Compare R = D/(1 + sin(A)) and y = (x^2)/(2*D) - D/2
- Q05 | - Compare R = D/(1 - sin(A)) with y = a*x^2 + b*x + c
- Q02 | - Compare R = D/(1 - sin(A)) with R = D/(1 - cos(A))
Q01. Diagram :
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Q02. Compare R = D/(1 - sin(A)) with R = D/(1 - cos(A))
R = D/(1 - sin(A))
- It is parabola with opening upward
- The directrix is at bottom
- It is equivalent to y = a*x^2 + b*x + c with a is positive
- It is parabola with opening rightward
- The directrix is at left side
- It is equivalent to x = a*y^2 + b*y + c with a is positive
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Q03. Compare R = D/(1 - sin(A)) and y = (x^2)/(2*D) - D/2
R = D/(1 - sin(A))
- D = distance from focus to directrix
- It is parabola and opens upward (A = 90 degrees y = infinite)
- Focus is (0, 0)
- Vertex is (0, -D/2)
- Equation of dirctrix is y = -D
- D = distance from focus to directrix
- It is parabola and opens upward
- Focus is (0, 0)
- Vertex is (0, -D/2)
- Equation of dirctrix is y = -D
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Q04. Compare R = D/(1 + sin(A)) and y = (x^2)/(2*D) - D/2
R = D/(1 + sin(A))
- D = distance from focus to directrix
- It is parabola and opens down (A = 270 degrees y = infinite)
- Focus is (0, 0)
- Vertex is (0, +D/2)
- Equation of dirctrix is y = +D
- D = distance from focus to directrix
- It is parabola and opens upward
- Focus is (0, 0)
- Vertex is (0, -D/2)
- Equation of dirctrix is y = -D
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Q05. Compare R = D/(1 - sin(A)) with y = a*x^2 + b*x + c
Solution
- Change y = a*x^2 + b*x + c to vertex form
- That is y = ((x - h)^2)/(2*D) - D/2
- Hence a = 1/(2*D)
- Translate to make h = 0
- The question now is same as Q03
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