First term scheme of work subject: technical drawing

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TD Note

Opening
PARABOLA
This is the locus of a point which moves such that its distance from a fixed point called focus and fixed straight line called directrix are always equal.
The ratio is called eccentricity
It means
I.e. The eccentricity of a parabola is unity or 1 (one)

To draw a parabola, Given the span and Height. Span = 80mm, Height = 50mm.
Procedure:

Using the span as length and the height as the width, construct a rectangle BCDE.
Divide AB and AC into the same number of equal parts.
Bisect DE to locate the vertex
Divide BA and AC into the same number of equal parts
Draw horizontal lines on all the divisions on BA and AC
Radiate lines from O to each of the divisions on DB and EC
Join the points of intersection of the vertical lines each side of O with their corresponding radial lines from O to get the parabola.

To construct a parabola given the directrix and focus
Procedure:

Draw the directrix DD and bisect it to get the axis.
Locate the focus F on the axis
Bisect PF to get the vertex V
Bisect line VF to get I. use radius VI it step off other units.
Draw perpendiculars to the axis on all the units 1 – n
Centre at F radii P1, P2, P3 etc draw arcs to cut the corresponding vertical lines 1, 2, 3 etc above and below.
Join the points of intersection to get parabola.

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To find the focus and directrix of a parabola
Procedure:

Draw the given parabola with AB as the span.
Bisect the span AB at x to get the axis Xd
At any point p on the axis erect a perpendicular from Z to the axis xv to get the focus F
Join Vy to get Z. drop a perpendicular from Z to the axis xv to get the focus F.
Centre at V radius VF cut the axis at d
A perpendicular to the axis at the point D gives the directrix.

Fig

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