The equation of the circle circumscribing the ΔAMB is

Engineering

Mathematics

Normal to Parabola

Question

x² + y² – 5x – 6y + 14 = 0

x² + y² – 3x – 5y + 8 = 0

x² + y² – 4x – 6y + 11 = 0

x² + y² – 6x – 7y + 20 = 0

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L₁ : 5x – y – 3 = 0
L₂ : x + 5y – 11 = 0

since, L₁ and L₂ are perpendicular
∴ they meet on the directrix
Also point of intersection of L₁ and L₂ is (1, 2).
M(3, 4) lies on the axis of the parabola.

Equation of circumcircle of ΔAMB is
⟹ (x – 1) (x – 3) + (y – 2) (y – 4) = 0
x² + y² – 4x – 6y + 11 = 0

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