Question

A focal chord is drawn on the parabola $y^2=8x$. if one end of it is (8,8) what is the other end?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

This can be done in 2 methods. Of these the better one would be to make use of specialties of focal chord in its parametric form.

In this straight forward method we take the equation of line and solve with that of parabola to obtain the second point.

Focus = (2, 0)

Equation of focal chord is, (y - 0) = (x - 2)

y = (x - 2)

3y = 4x - 8

4x - 3y - 8 = 0

Solving with parabola $y^2=8x$

$y^2=8\left[\frac{3y+8}{4}\right]\left(2\right)$

$y^2-6y-16=0$

$y=\frac{6\pm \sqrt{36+64}}{2}=\frac{6\pm 10}{2}=8or-2$

$\therefore otherpoint\Rightarrow [\frac{1}{2},-2]$