﻿ Tangents drawn from the point P(1, 8) to the circle x2 + y2 – 6x – 4y – 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle in PAB is : Kaysons Education

# Tangents Drawn From The Point P(1, 8) To The Circle x2 + y2 – 6x – 4y – 11 = 0 Touch The Circle At The Points A and B. The Equation Of The Circumcircle Of The Triangle In PAB is

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## Question

### Solution

Correct option is

x2 + y2 – 4x – 10y + 19 = 0

Equation of AB the chord of contact of p is

1.x + 8y – 3(x + 1) – 2(y + 8) – 11 = 0

Equation of any circle through. AB is

x2 + y2 – 6x – 4y – 11 + λ(x – 3y + 15) = 0

It will pass through P (1, 8) if

1 + 64 – 6 – 32 – 11 + λ(1 – 24 + 15) = 0

Thus, equation of the required circle is

x2 + y2 – 6x – 4y – 11 + 2(x – 3y + 15) = 0

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