Question

If one end of the diameter is 1,1 and other end lies on the line x +y = 3,then locus of centre of circle is​

Answer 1

Answer:

2x+2y=5

Step-by-step explanation:

Let the other end be (t,3−t).

So, the equation of the variable circle is  

(x−1)(x−t)+(y−1)(y−3+t)=0

⇒x 2 +y2 −(1+t)x−(4−t)y+3=0

∴ The centre (α,β) is given by

α=  2 1+t ,β= 2 4−t ⇒2α+2β=5

Hence, the locus is 2x+2y=5