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Find all the tangents to a circle (x-a) 2 + (y-b) 2 = r 2 which make an angle @ with x axis

Find  all the tangents to a circle 
(x-a)2 + (y-b)2 = r2
which make an angle @ with x axis
 

Grade:11

5 Answers

Abhishek Singh
105 Points
9 years ago
any line of form 
y-b=mx-g +/- r(1+m2)½                               ( here +/- means plus or minus)
will touch the given circle,
if we put m=tan@ then the equation of the lines are the required tangents. 
Kaustubh Nayyar
27 Points
9 years ago
BUT THE answer is
(x-a)cos@ + (y-b)sin@ = + r                     ( + means plus minus)
Abhishek Singh
105 Points
9 years ago
sorry it must be y-b=m(x-a) +/- r(1+m2)½              ( here +/- means plus or minus)
 
in above post g must be replaced by “-a” and m is multiplied to x-a. it was my fault
But your answer is wrong as the slope of you
Abhishek Singh
105 Points
9 years ago
as the slope of your line is -cot@, but as the lines make angle @ with x axis its slope must be tan@.
Abhishek Singh
105 Points
9 years ago
the result is very simple 
for circle centred at origin we say eqn of tangents is   y=mx +/- r(1+m2)1/2 
for circle with centre a,b   we can linearly transform the eqn. by
Replacing y------> y-b
               x----------> x-a 

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