if one point of a focal chord of a parabola x^2-8y=0 is (-4,2), what will be the other end of the focal chord.

I think that this answer is wrong

To find the other end of the focal chord, we can use the concept that the midpoint of the focal chord lies on the axis of the parabola, which is given by the equation x = 0.

Given that one point of the focal chord is (-4, 2), we can find the midpoint by finding the average of the x-coordinates and the y-coordinates of the given point and the other end.

Let the other end of the focal chord be (a, b).

Using the midpoint formula:
Midpoint(x-coordinate) = (-4 + a) / 2 = 0

Solving this equation for 'a':
-4 + a = 0
a = 4

Hence, the x-coordinate of the other end of the focal chord is 4.

Now, let's find the y-coordinate of the other end using the equation of the parabola: x^2 - 8y = 0

Substituting x = 4 into the equation:
4^2 - 8y = 0
16 - 8y = 0
8y = 16
y = 2

Therefore, the other end of the focal chord is (4, 2).

To find the other end of the focal chord, we need to find the point where the focal chord intersects the parabola.

The equation of the parabola is given as x^2-8y=0. We can rewrite it in terms of y:

8y = x^2

y = x^2/8

Now, let's substitute the coordinates of the known point (-4, 2) into the equation to find the value of x:

2 = (-4)^2/8
2 = 16/8
2 = 2

So we have x = -4 as the x-coordinate of the known point.

Now, let's substitute this value back into the equation of the parabola to find the corresponding y-coordinate:

y = (-4)^2/8
y = 16/8
y = 2

Hence, the other end of the focal chord will have coordinates (-4, 2).

Therefore, both endpoints of the focal chord are (-4, 2).

Given: x^2 - 8y = 0. FC(-4,2).

8y = x^2,
y = (1/8)x^2, y-parabola.

h = Xv = -b/2a = 0/2a = 0.
k = Yv = 0^2/8 = 0.

V(h,k) = (0,0).

F(0,y)

V(0,0)

a = 1/8.
4a = 1/2.
1/4a = 2.

y = k + 1/4a = 0 + 2 = 2.

FC = 1/a = 8/1 = 8.

FC: (-4,2), F(0,2), (X2,2).
X2 -(-4) = 8,
X2 + 4 = 8,
X2 = 8-4 = 4.

FC: (-4,2),(4,2).