Question

A line passing through P(6, 4) meets the coordinates axes at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is ? ​

Answer 1

Step-by-step explanation:

Given A line passing through P(6, 4) meets the coordinates axes at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is ?  

• Consider the coordinate axis and there is a line passing through the point (6,4) and meets the coordinate axis at A and B. O is the origin.
• We have the centre of circumcircle of a right angled triangle OAB is midpoint of hypotenuse.
• We need to find the locus of the midpoint.
• Let the midpoint of AB be (h,k), so the point A (2h,0) and B(0,2k)
• So coordinates of A(2h,0) and B(0,2k)
• Now equation of the line passing through the two points will be
•                  x / 2h + y /  2k = 1
• So this line is passing through (6,4)
•                 6 / 2h + 4 / 2k = 1
•                 3/h + 2/k = 1
• Therefore locus of midpoint that is circumcentre of triangle will be
•                   3/x + 2/y = 1
•                Or 3x^-1 + 2y^-1 = 1

Reference link will be

https://brainly.in/question/15909040

Answer 2

Answer:

Upper answer is correct

hope it helps