the line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle.

Dear Simran,

well you could first find the radius at (3,-4) since it is perpendicular to the tangent
that''s using two-points form: (for (0,0) and (3,-4) )
y + 4 = [(-4 -0) / (3 - 0 )]* (x - 3)
or, 3y + 12 = -4x + 12
or, y = (-4/3) x
let m be the slope of the tangent, then:
m * -4/3 = -1
or, m = 3/4
thus you use the equation:
y - y, = m (x - x,)
or, y + 4 = 3/4 (x - 3)
or, 4y + 16 = 3x - 9
or, 3x - 4y - 25 = 0
that''s the slope you need
of course, if you wanted to do it the shorter way, you could always use the formula:
ax + by = r^2
where (a,b) is the point (3,-4) and r is the radius squared, as in the circle''s equation x^2+y^2 = r^2, which is 25

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. 

http://www.askiitians.com/packages/packages.aspx

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert