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If a double ordinate of the parabola y 2 =28x subtends a right angle at its vertex then what will be the length of its double ordinate...?

If a double ordinate of the parabola  y2=28x subtends a right angle at its vertex then what will be the length of its double ordinate...?

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
The 2 ends of the double ordinate will be meeting the parabola at P(c,d) and Q(c,-d).
The line segments joining P and Q with the vertex will have slopes as negative reciprocals of each other. Find the relation between c and d using this as the vertex is at origin. Use this relation in the parabola equation to get the value of y at P and Q(this time not in terms of c and d but in terms of ‘a’... y2=4ax)

The value of y will give the value of ordinate. Twice this length will be the length of the double ordinate.

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