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Q01 |
- Diagram : Sketch parabola using ruler
- Q02 | - Sketch parabola using ruler
- Q03 | - Convert y = (x^2)/(2*D) - D/2 to polar form
- Q04 | - Convert y = x^2 to polar form
- Q05 | - Sketch tangent to parabola
- Q05 | - Reference
- Q02 | - Sketch parabola using ruler
Q01. Diagram : Parabola
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Q02. Sketch parabola using ruler
Graph of y = 0.5*(x^2)
- 1. Find focus to directrix : D = 1/(2*a) = 1
- 2. Find Vertex
- xv = 0
- yv = 0
- 3. Find focus
- xf = 0
- yf = yv + D/2 = 0.5
- 4. Draw line of directrix and focus on graph paper
- 5. Draw a point Q on directrx
- 6. Draw line PQ and perpendicular to directrix
- 7. Join Q and F
- 8. Bisect line QF and bisector meets PQ at P
- 9. Since PF = PQ, hence P is a point on parabola
- 10 Repeat steps 5 to 9 for more points
- 11 Join all points and it is the required parabola
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Q03. Convert y = (x^2)/(2*D) - D/2 to polar form
Method 1
- R = D/(1 - sin(A))
- Focus F at (0, 0)
- Vertex at (0, -D/2)
- Parabola open upward
- y = (x^2)/(2*D) - D/2
- Vertex at ( 0, D/2)
- Focus at (0, 0)
- Parabola open upward
- Hence the polar form is R = D/(1 - sin(A))
- y = (x^2)/(2*D) - D/2
- 2*D*y = x^2 - D^2
- Add y^2 on Both sides
- y^2 + 2*D*y + D^2 = x^2 + y^2
- Since R^2 = x^2 + y^2 and y = R*sin(A)
- (y + D/2)^2 = R^2
- (R*sin(A) + D/2)^2 = R^2
- Square root on both sides
- R^2 - R*sin(A) = D/2
- R = (D/2)/(1 - sin(A))
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Q04. Convert R = D/(1 - sin(A)) to rectangular form
- Polar coordinates
- R^2 = x^2 + y^2
- y = R*sin(A)
- R*(1 - sin(A)) = D
- R - R*sin(A) = D
- x^2 + y^2 = (y + D)^2
- x^2 + y^2 = y^2 + 2*D*y + D^2
- x^2 = 2*D*y + D^2
- y = (x^2)/(2*D) + D/2
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Q05. Sketch tangent to parabola
Diagram and method
- Subject | Sketch by ruler
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Q06. Reference
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