Question

Length of the double ordinate of the parabola $y^{2} = 4x$, at a distance of 16 units from its vertex is

A. 4

B. 8

C. 16

D. 12

✨ Free AI Tools for You

Powered by Chatterbot AI

Answer

To determine the length of the double ordinate of the given parabola ( y^2 = 4x ) at a distance of 16 units from its vertex, follow these steps:

  1. Identify the Parameters of the Parabola:

    • The equation of the given parabola is ( y^2 = 4x ).

    • This can be compared with the standard form ( y^2 = 4ax ), which results in ( 4a = 4 ), leading to ( a = 1 ).

    • The vertex of the parabola is at ( (0,0) ) and its focus is at ( (a,0) = (1,0) ).

  2. Distance from the Vertex:

    • We are given that the distance from the vertex is 16 units. In terms of the parabola, this distance is represented by ( a t^2 ).

    • Substituting ( a = 1 ): $$ t^2 = 16 \Rightarrow t = \pm 4 $$

  3. Length of the Double Ordinate:

    • The formula for the length of the double ordinate at a distance ( at^2 ) from the vertex is ( 2|y| ), which corresponds to ( 4at ) when derived using the general properties of the parabola.

    • Substituting ( a = 1 ) and ( t = 4 ): $$ 4at = 4 \cdot 1 \cdot 4 = 16 $$

Thus, the length of the double ordinate at a distance of 16 units from the vertex is 16 units.

Therefore, the correct option is C. 16.


Was this helpful?

India's 1st AI Doubt Solver for CBSE, JEE, and NEET

Ask a Question for Free

and then it's just ₹212 a month