Question

In the parabola y² = 4ax, the length of the chord passing through the vertex and inclined to the axis at is π/4 is : 

A. 4√2a 

B. 2√2a 

C. √2a 

D. none of these

Answer 1

Option : (A)

Given that,

We need to find the length of the chord of the parabola y² = 4ax which passes through the vertex and is inclines to axis at π/4.

We know that,

The vertex and axis of the parabola y² = 4ax is (0, 0) and y = 0(x - axis). 

We know that,

The equation of the straight line passing through the origin and inclines to the x - axis at an angle θ is y = tanθx.

⇒ y = tan(\(\frac{\pi}{4}\))x

⇒ y = 1.x 

⇒ y = x. 

The equation of the chord is y = x. 

Substituting y = x in the equation of parabola. 

⇒ x² = 4ax 

⇒ x = 4a. 

⇒ y = x = 4a 

The chord passes through the points (0, 0) and (4a, 4a). 

We know that,

The distance between the two points (x₁, y₁) and (x₂, y₂) is \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).