Find the co-ordinates of the middle point of the chord of the parabola y2 = 16x, the equation of which is 2x – 3y + 8 = 0

To find the coordinates of the middle point of the chord of the parabola y^2 = 16x, we need to first find the equation of the chord.

Given that the equation of the chord is 2x - 3y + 8 = 0, we can rewrite it in terms of y:

2x - 3y + 8 = 0 -3y = -2x - 8 y = (2/3)x + (8/3)

Now, let's find the coordinates of the middle point of the chord. The middle point of a chord is the midpoint between its two endpoints.

To find the midpoint, we need the coordinates of two points on the chord. Let's choose two arbitrary values for x and find the corresponding y values.

Let's choose x = 0: y = (2/3)(0) + (8/3) = 8/3

So, one point on the chord is (0, 8/3).

Now, let's choose another value for x. Let's choose x = 3: y = (2/3)(3) + (8/3) = 2 + 8/3 = 14/3

So, another point on the chord is (3, 14/3).

Now, we can find the midpoint of the chord using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the coordinates of the two points we found, we get:

Midpoint = ((0 + 3)/2, (8/3 + 14/3)/2) Midpoint = (3/2, 22/6) Midpoint = (3/2, 11/3)

Therefore, the coordinates of the middle point of the chord of the parabola y^2 = 16x, with the equation 2x - 3y + 8 = 0, are (3/2, 11/3).