Given that a circle passes through the points P(3,5) and Q(-1,3) has a radius square root of 10, find the eqn of the circle

aruv | Student

We have given two points P(3,5) and Q(-1,3). Also radius of the circle `sqrt(10)`  unit.  We wish to dertermine equation of the circle.

Let equation of the circle whose centre at (h,k) and radius r be

`(x-h)^2+(y-k)^2=r^2`      (i)

(i) posses through P and Q ,therefore


`` `9+h^2-6h+25+k^2-10k=10`

`h^2+k^2-6h-10k=-24`    (ii)



`h^2+k^2+2h-6k=0`       (iii)

Solving (ii) and (iii),we have


k=6-2h     (iv)

put k ,from(iv) in (iii)




`h=0 or h=2`

h=0 then k=6

h=2 then  k=2

Thus there are two circles








Hence we have two circle.