Quandaries
and Queries 

The equation of a hyperbola is 32x*2 18Y*264x +72y +248=0. The equation of a tangent line to this hyperbola is y= (16/15)X + 10/3 I have been trying to find the point where this line intersects the graph. What I did was solve for x and then plugged in the result into the equation of the hyperbola, but I am getting two answers and I am supposed to get only one because the line is tangent to the graph. For this reason, I would like to know what I am doing wrong or what I have to do to know which answer is correct. 

Hi, Your technique is fine, you must have an algebra error. I followed your instructions and solved the equation of the tangent line for x getting
I substituted this value into the equation of the hyperbola and simplified to get
and hence y = ^{26}/_{3} I find that sometimes I make the same algebra error again and again so in this situation I would try a different attack. Rather than solving the tangent line equation for x, just substitute
into the equation of the hyperbola and solve for x. Doing it this way I got
and hence x = 5. Penny 

