a fixed point is 60mm from the fixed straight line. draw the curve when eccentricity is 2/3.name the curve. draw tangent and normal to the curve through a point p which is 65mm from the straight line
Answers
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Steps for Construction of Ellipse.
Solution: a)
1. Draw a vertical line DD to represen the directrix.At any point C on it draw a line perpendicular to the directrix to represer the axis CC'.
2. Distance between the focus and the din trix is 60 mm. Hence mark F1. the focus such that
CF1=160mm.
3. e 2/3 So construct a right angled ▲ XY such that XY / C * X = 3units / 4 * units (X is any; int on the axis).
4. From F1 draw a 45° line to cut CY at S.Fro IS
erect Vertical to intersect CF1 at V1, the ver ex
Now SV1=F1V1 .
5. ACXY is similar to ACVIS.
::SV1/CV1=XY/CX=F1V1/CV1=2/3
6. From F1 draw another 45° line to interse the extension of CY at T. From T erect vertical t intersect the axis at V2. another vertex. V1V2
Major Axis.
7. Along the major axis, mark points 1.2.....10 at approximately equal intervals. Through these points erect verticals to intersect CY (produced if necessary) at 1^ prime .2^ prime ..10^ prime
8. With 11' as radius and F1 as centre draw two arcs on either side of the axis to intersect the vertical line drawn through 1 at P1 and P1'.
9. With 22' as radius and F1 as centre draw two arcs on either side of the axis to intersect the vertical line drawn through 2 at P2 and P2'.
10. Repeat the above and obtain P3 and P3^ prime ,...,P10 and P10' corresponding to 2.3.10 respectively. Draw a smooth ellipse passing through V1.P1P10.V2.P10 P1'.V1.
11. To mark another Focus F2: Mark F2 on the axis such that V2F2=V1F1 .
12. To mark another Directrix D^ prime D^ prime :Mark C^ prime along the axis such that
CV2=CV1 . Through C' draw a vertical line D'D'
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