ANAIYIK :/,) VIII. 



and its slope is, therefore, \rt. f>s < 



Hence the reqniivd r<jiiati<>n >f the corresponding normal 

 at /', i* < Arts. 53, 62) 



EXERCISES 



1. I> (I..- liiM-:J.r + 2y = 17 tangent to the ellipse 16 z + 25 y = 400? 



2. Find the equation of a tangent to the conic z 2 + 5y 2 3z + 1 

 -4=0, parallel to the line y = 3 x + 7 (cf . Art. 8 



Write the equations of the tangent and normal to each of the foll<>\\ 

 ing conies, through a point (x v y^ on the curve (cf. Art. 122 [50]). 



z* v 2 



? + & = '. 



T* II* 



S-S- L 



5. z 1 = 4j (y 5) ; sketch the figure. 



6. 3z 2 - 5y 2 + 24 z = 0; sketch the figure. 



7. z* + 5y* - 3z + lOy - 4 = 0; sketch the figure. 



8. Derive, by the secant method (cf. An. li'J), the tangent to t 

 parabola y* = 4/>z; the point of contact being (*,, yj. 



9. Derive, by the secant method, the tangent t th ellipse z 2 I //* 

 8z-f20y = 0; the point of contact being (z,, ;/,). 



Write the equations of the tangents ami normals to each of the fol- 

 lowing conies, at the given point : also sketch each figure: 



10. 9z*+5y* + 36z + 20y + 11 = 0, at the point (-2, 1); 



11. 9r + 4y* + 6z + 4y = 0, at the point (0. 0); 



12. y*-6y-8z = 31, at the point ( :\. 1); 



Since the equation of the nornial [51] is so readily deduced, in \n 

 particular case, from that of the tangent, and since the latter is so ef 

 remembered, it is not recommended that equation [61] be memorized. 



