Findall the tangents to a circle (x-a)2 + (y-b)2 = r2which make an angle @ with x axis
Kaustubh Nayyar , 9 Years ago
Grade 11
Differential Calculus> Find all the tangents to a circle (x-a) 2...
5 Answers
Abhishek Singh
Last Activity: 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
Last Activity: 9 Years ago
BUT THE answer is
(x-a)cos@ + (y-b)sin@ = + r ( + means plus minus)
Abhishek Singh
Last Activity: 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
Last Activity: 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
Last Activity: 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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