M 



hf Moment of any tangent to an hyperbola 

 the inymytotct u Meected by the point of cent / 

 The tangent (8) hat the intercept* on the z-axU and y 



or -2 av or-2 yi . 

 Thru or- 0r~ . . . (4) 



,.y,) is a point f tin* liy|vrbola 



0r-0r'-a + 6 . . . 



. fhe rectangle formed by the intercept* which any tangent 

 to the hyperbola makee upon the atymptoUe it eonetant; it it 

 equal to the turn of the njuar npon the lemi-ajrs . 



Moreover, equation (5) in y 1. written 



but 



. ^y 



hence (fi) Incomes ^- L -^- -in 2 ^ = a6 ; .... (7) 



that in, the triangle formed by any t :ngent to an hyperbola 

 and it* atymjttotci ie conetant ; it it equal to the rectangle 

 /xm the eemi-axee. 



EXERC'SES 



1 Ki...l r i,,. .^nation of the hyperbola 9 x - 16f* = 25 when referred 

 to its asymptotes M axes. 



2 Find the serai-Axes, eccentricity, and the vertices, of the hyperhola 

 sy as 4, the angle between the axes (asymptotes) being 90*. 



3. Find the semi-axes, eccentricity, rertiees, and the foci, of the hyper- 

 bola ry = - 12. the angle between the axes being flO. 



4. Prove that the segments of any line which are intercepted lutnesji 

 an hyperbola and its asymptotes are equal 



