<PRE><B>Question 1165039</B>
&lt;br&gt;
Draw a graph with the origin on the ground halfway between the two poles.&lt;br&gt;
Then the vertex of one branch of the hyperbola is at (0,68), and one other point on that branch is (10,70).  We are to find the point (7,y).&lt;br&gt;
The equation of the hyperbola is&lt;br&gt;
{{{y^2/a^2-x^2/b^2 = 1}}}&lt;br&gt;
{{{y^2/68^2-x^2/b^2 = 1}}}&lt;br&gt;
The numbers in the problem are not &quot;nice&quot;; you will need a calculator to solve the problem.&lt;br&gt;
You won&#39;t learn anything by having me do the calculations for you, so I leave that to you.&lt;br&gt;
(1) Use the coordinates of the other point (10,70) in that equation to find b^2.&lt;br&gt;
(2) Plug that value of b^2 in the equation, then solve for y when x=7.&lt;br&gt;
Note: my answer, which is reasonable, is 68.987 to 3 decimal places&lt;br&gt;
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