Question

Find equation of vcircle which passes through point 1,-2 4,-3 and whoes centre lies on

Answer 1

000000000000000000000000000000000000000000

equation of circle with (1,−2)and as (4,−3)diameter,

(x−1)(x−4)+y+2)(y+3)=0(1)

Equation of line joining (1,−2)and as (4,−3)

(4–1)(y+2)−(−3+2)(x−1)=0⟹

3y+x+5=0(2)

equation of family of circles passing through the 2 points is

(x−1)(x−4)+(y+2)(y+3)−2K(3y+x+5)=0⟹

x2+y2–2(K+52)x−2(3K−52)y+10–10K=0(3)

The center is (K+52,3K−52)

This should lie on 3x+2y=7⟹

3(K+52)+2(3K−52)=7⟹2K=1

(3) now becomes

x2+y2–6x+2y+5=0