a)find the equations of the tangent lines to the circlex^2+y^2=25 at the points where x = 4.

b) find the equations of the normal lines to this circle atthe same points . ( the normal line is perpendicular to the tangentline at that point)

c) at what points do the two normal lines intersect?

can i please get a detailed worked out solution, so i get theconcept and know how to do other problems on my own?i'd be verygrateful and give you an A.thanks!

## Answers ( 1 )

_{1},y_{1}= 4,3 andother at x_{2},y_{2}=4,-3_{1}= slope of first tangent = -4/3_{2}= slope of second tangent = 4/3y-Y = m(x-X) where X,Y donates the pointsx

_{1},y_{1}andx_{2},y_{2}I have already found the points. Now plug the values in the eqngiven below to get the eqn of normal (two normals)

the normal is given by:

y-Y = (-1/m)(x-X)

c) at what points do the two normal lines intersect?

The wo normals that you get are

3x-4y= 0.........................................(3)

and 3x+4y=0....................................(4)

solving eqn 3 and 4 u get x,y = 0,0 therefore the normalsmeet(intersect) at the origin.

Note: both the eqns of normal are independent of constant terms,which means they are passing through origin.

Let me know if u face any difficulty