SOLUTION: Find the equation of the circle whose centre lies on the line x = 2y, passes throught the point (2,5), and for which the lenght of the tangent from the origin is sqrt{ 7)}}. Please

Question 990644: Find the equation of the circle whose centre lies on the line x = 2y, passes throught the point (2,5), and for which the lenght of the tangent from the origin is sqrt{ 7)}}. Please recomend any coordinate geometory textbook for me
Answer by anand429(138) (Show Source): You can put this solution on YOUR website!
Since centre lies on x=2y,
Let the centre be (2a,a)
Eqn of circle will be

Since it passes through (2,5), putting it we get,

=>
=> ----------------------------------------(i)
Now length of tangent from origin is sqrt(7)
So, using pythagoras theorem,
(Distance of centre from origin)^2 = (length of tangent)^2 + (radius)^2
=>
=> -----------------------------(ii)
Subtracting (i) from (ii),

=>
Putting back in eqn (ii),

Putting both values in eqn of circle we get,

=>
P.S. - "The Elements of Coordinate Geometry" by S. L. Loney
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