Question

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

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 

                                                                   

SIMILAR QUESTIONS

Q1

 

If a circle passes through the point (ab) and cuts the circle x2 + y2 = k2 orthogonally, equation of the locus of its centre is

Q2

Equation of the circle which passes through the origin, has its centre on the line x + y = 4 and cuts the circle

x2 + y2 – 4x + 2y + 4 = 0 orthogonally, is

Q3

If O is the origin and OPOQ are distinct tangents to the circle x2 + y2 + 2gx + 2fy + c = 0, the circumcentre of the triangle OPQ is

Q4

The circle passing through the distinct points (1, t), (t, 1) and (tt) for all values of t, passes through the point

Q5

If OA and OB are the tangents from the origin to the circle x2 + y2 + 2gx + 2fy + c = 0, and C is the centre of the circle, the area of the quadrilateral OACB is 

Q6

The angle between a pair of tangents drawn from a point P to the circle x2 + y2 + 4x – 6y + 9 sin2α + 13 cos2α = 0 is 2α. The equation of the locus of the point P is

Q7

Equation of a circle through the origin and belonging to the co-axial system, of which the limiting points are (1, 2), (4, 3) is

Q8

If a line segment AM = a moves in the plane XOY remaining parallel toOX so that the left end point A slides along the circle x2 + y2 = a2, the locus of M is

Q9

If common chord of the circle C with centre at (2, 1) and radius r and the circle x2 + y2 – 2x – 6y + 6 = 0 is a diameter of the second circle, then the value of r is  

Q10

Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is