# 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

## 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:

**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) ).

**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 ): $$ t^2 = 16 \Rightarrow t = \pm 4 $$

**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**.

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

and then it's just ₹212 a month