Equation of Tangent to y² = 8x at the end of the latusrectum in 4th quadrant is

Solution:

Identify the standard form of the parabola:

The given equation is y² = 8x, which is in the standard form y² = 4ax.

Determine the value of a:

By comparing y² = 8x with y² = 4ax, we find that 4a = 8, so a = 2.

Find the coordinates of the end of the latus rectum:

The latus rectum of a parabola y² = 4ax has endpoints at (a, ±2a).

For a = 2, the endpoints are (2, 4) and (2, -4).

Determine the equation of the tangent at (2, -4):

The general equation of the tangent to the parabola y² = 4ax at the point (x₁, y₁) is:

y * y₁ = 2a * (x + x₁) 

Substituting a = 2, x₁ = 2, and y₁ = -4 into this equation:

-4y = 4(x + 2) 

Simplifying:

-4y = 4x + 8 

Thus, the equation becomes:

x + y + 2 = 0