Problems On Parabola

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 PARABOLA BY RECTANGLE METHOD, METHOD OF TANGENTS AND DIRECTRIX-FOCUS METHOD.

 RECTANGLE METHOD...

1. A ball thrown in air attains 100 m height and covers horizontal distance 150 m on the ground. Drew the path of the ball(projectile).

STEPS:

  1. Draw a rectangle of the above size and divide it into two equal vertical parts

  2. Consider left part fir construction divide height and length in an equal number of parts and name those 1,2,3,4,5 & 6

  3. Join vertical 1,2,3,4,5 & 6 to the top center of the rectangle

  4. similarly draw upward vertical lines form horizontal 1,2,3,4,5 and wherever these lines intersect previously drawn inclined lines in sequence mark those points and further join in smooth possible curve.

  5. Repeat the construction on the right side rectangle also. Join all sequence. This locus is parabola.


parabola by rectangle method problem no 3
 METHOD OF TANGENTS...

2. Draw an isosceles triangle of 100 mm long base and 110 mm long altitude, Inscribe a parabola in it by method of tangents.

SOLUTION STEPS:

  1. Construct triangle as per the given dimensions.

  2. Divide it's both sides into the same no.of equal parts.

  3. Name the parts in ascending and descending manner, as shown.

  4. Join 1-1, 2-2, 3-3, and so on.

  5. Draw the curve as shown i.e. tangent to all these lines. The above all lines being tangents to the curve, it is called the method of tangents.


parabola by method of tangents problem no 2
DIRECTRIX-FOCUS METHOD...

3. Point F is 50 mm from a vertical straight line AB. Drew locus of point P, moving in a plane such that it always remains equidistant from point F and line AB.

SOLUTION STEPS:

  1. Locate the center of the line, perpendicular to AB from point F. This will be the initial point P and also the vertex.

  2. Mark 5 mm distance to its right side, name those points 1,2,3, and from those drew lines parallel to AB.

  3. Mark 5 mm distance to its left of P and name it 1.

  4. Take O-1 distance as radius and F as center draw an arc cutting first parallel line to AB. Name upper point P1 and lower point P2(FP1=O1)

  5. Similarly repeat this process by taking again 5 mm to right and left and locate P3P4.

  6. Join all these points in a smooth curve.


parabola by directrix-focus method problem no 3
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