Q Let PA and PB are two tangents drawn from point p on the line x+2y=3 to the circle - Maths - Conic Sections

Question

Q Let PA and PB are two tangents drawn from point p on the line
x+2y=3 to the circle x - 1 2 + y - 1 2 = 1 , then find the locus of
the circum centre of triangle PAB

Varun Rawat · Accepted Answer

Let Pa,b be the point
Since, P Lies on the line x+2y = 3, then it must satisfy it
Now, a + 2b = 3 ⇒b = 3-a2Now, coordinates of P are a, 3-a2Now, circle passes through P, A, B and also passes through the centre of x - 12 + y - 12 = 1
The coordinates of centre of circle  x - 12 + y - 12 = 1 are : O1,1Now, centre of circumcircle is mid point of OP
i e
 a+12, 3-a2+12 = a+12, 5-a4Let x = a+12 and  y = 5-a4⇒a = 2x - 1   and  a = 5 - 4ySo, 2x - 1 = 5 - 4y⇒2x + 4y = 6⇒x + 2y = 3This is the required equation of locus

Q. Let PA and PB are two tangents drawn from point p on the line x+2y=3 to the circle x - 1 2 + y - 1 2 = 1 , then find the locus of the circum centre of triangle PAB.

Q. Let PA and PB are two tangents drawn from point p on the line x+2y=3 to the circle ${(x - 1)}^{2} + {(y - 1)}^{2} = 1$ , then find the locus of the circum centre of triangle PAB.