Ellipse Construction by Focus Directrix Method

Given Data:

• Distance of the focus from the directrix: 50 mm
• Eccentricity: 2/3

Steps to Construct the Ellipse:

Step 1:

• Draw a vertical line labeled AB.
• From point C on line AB, draw a horizontal line.

Step 2:

• Mark a point F at a distance of 50 mm from point C.
• Divide the line segment CF into five equal parts (sum of numerator and denominator of eccentricity).

Step 3:

• Mark the vertex V on the second division point from F.

Step 4:

• From V, draw a perpendicular line.
• Mark point E such that VF equals VE.
• Join ZE and extend it.

Step 5:

• Divide the line to the right of F into equal parts.

Step 6:

• Drop perpendiculars from these respective points.

Step 7:

• Measure distance 1-1' and draw an arc from point F on either side.
• Similarly, for distance 2-2', draw arcs from point F on either side.
• Continue for other points (3, 4, etc.) and draw arcs similarly.

Step 8:

• Using a French curve, connect the points to form the required ellipse.

Drawing Tangent and Normal at Point Q:

Step 9:

• Consider point Q anywhere on the ellipse.
• Join point Q to F.

Step 10:

• Construct a 90-degree angle with line QF at point F.
• Extend this line to meet the directrix at point T.

Step 11:

• Join point T to Q and extend this line. This line is tangent to the ellipse at point Q.

Step 12:

• From point Q, draw a perpendicular line. This line is normal to the curve.

Conclusion:

• The steps above describe how to construct an ellipse using the focus directrix method, along with drawing the tangent and normal at any point Q on the ellipse.