# Parabolic Cable Suspended; Inconsistent Latus Rectum and Equation of Line

For a National Board Exam Review:

A cable suspended form supports that are the same height and 600ft apart has a sag of 100ft. If the cable hangs in the form of a parabola, find its equation taking the origin and the lowest point.

Answer is A. ${x^2 = 900y}$

Ok, I know the Latus Rectum is 4a; I dont seem to get how it became 900? when a = 100; then isn't 4a = 400? therefore ${x^2 = 400y}$. Problem set maybe wrong; just making sure I'm not missing out on a concept... What am I doing wrong? What is right approach?

• We are taking the lowest point as the origin, and the horizontal line through the lowest point as the $x$-axis. Then the parabola has equation of the form $y=kx^2$. To find $k$, note that the parabola does through the point $(300,100)$. Substitute and solve for $k$. The answer $x^2=900y$ (or an equivalent form) is right. – André Nicolas Aug 17 '15 at 2:10

Let the equation of the parabola be $x^2=4ay$ by taking lowest point as the origin & vertical line through it as y-axis.
Now, the points of both the supports will be at $(-300, 100)$ & $(300, 100)$ which lie on the parabola hence, setting $x=300$ & $y=100$ in the equation we get $$(300)^2=4a(100)$$ $$4a=\frac{90000}{100}=900$$ Hence, setting the value of $4a$, the equation of the parabola is
$$\bbox[5px, border:2px solid #C0A000]{\color{red}{x^2=900y}}$$