Find the equation of the circle passing through the points A(4, 3), B(2, 5) and touching the axis of
y. Also find the point P on the y − axis such that the angle APB has largest magnitude.
Text Solution
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(x² + y² − 4x − 6y + 9 = 0 OR x² + y² − 20x − 22y + 121 = 0, P(0, 3), θ = 45°)
Equation of circle touching y - axis is x² + y² + 2gx + 2fy + 
= 0
it passes through (4, 3) & (2, 5)
so 
solving above two equations, we get (g, f) ≡ (–2, – 3) & (– 10, – 11).
So equations of circles are x² + y² – 4x – 6y + 9 = 0 and x² + y² – 20x – 22y + 121 = 0
for circle x² + y² – 4x – 6y + 9 = 0.
tan θ = 
= 
= 
So tan θ is max at k = 3 at k = 3, tan θ = 1 ⇒ θ = 45°
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