



149 



on of the normal to arh of lh eireles of 1 

 ^h the given |- 



4 \ Mi.jpnt u perpendicular to the radius drawn to ite | 

 ctMH.i 'ierive the equation of the tangent to 



'i )+(jr -)* *t the j /,) (ef.equatkm QW)). 



5 I rotn - t '.! ' thai a normal to a circle pissns through iU 



find thf : th- normal to the circle * + $-<! * + 8 jf + 21 



u.l il..- .-,,,,. ihon* of the two tangents, drawn through the ex- 

 tenial point (1 1, 3) to the circle * + f = 40. 



SraoKMjox. UM the equation of the tangent in term* of iU slope. 



7. \Vh:it is ih ..... piation of the circle whoee center is at the point 

 . and which touches the line 3* + 2y - 10 = 0? 



8. I'nder what condition will the line - + J = 1 touch the circle 



a o 



9. Find the equation of a circle inscribed in the triangle whose tides 



ar* the lines x = 0, y = 0, and * + J = 1. 



a o 



10. Solve Ex. 6 by amuming r, and y, as the coordinates of tha point 

 of contact, and then finding th.-ir numerical values from the two equa- 

 tions which they satisfy. 



86. Lengths of tangents and normals. Subtangents and 

 subnormals. The tangent an<l n. -nii.il lines of any curve 



.-I iinli-tinitrly in l..tl 

 directions ; it is, however, 

 'nient to consider as tin- 

 length of the tangent 



measured 

 tin- point M| intrrsTti(.n . 





of the tangent \\ith tli< 



>. .in-l Mtnil.uK to consider as the length of the normal 

 tin* Instil 7'j.V. measured from P, to the point of intei 

 (N) of the normal with the JHUUS. 



