Given an asymptote and three finite points on the conic, to determine the conic.
Draw through the point of contact P of the tangent AB two lines, one parallel to one asymptote and the other parallel to the other.
The area between the curve and its asymptote is 3[pi]a squared, i.
P will therefore be infinitely remote, and the point I having then reached t, where D T touches the smaller circle, C t S will be an asymptote to the curve.
Since DTO is a right angle, T lies upon the circumference of the circle whose center is C, and diameter DO; this circle cuts the asymptote SCS at M and N.
As D L E rises, the points P and Q recede from A and B, the points L and E approach each other, finally coinciding at T; at this instant I and J fall together at t, so that S S is the common asymptote to A P and B Q.
Of these Hyperbola's oneAsymptote is the line DE, and their other Asymptotes are parallel to the lines CA and CB.
If these factors are all real and distinct, there is an asymptote corresponding to each factor.
