Question

11. Find the equation of the circle which passes through (2, 4)
and whose centre is the intersection of the lines x - y=4
and 2x +3y=-7.​

Answer 1

Answer:

The equation of the given lines are :

x-y=4…(i)

2x+3y=-7… (ii)

Solving (i) and (ii) simultaneously, we get x=1andy=-3

So, the point of intersection of the given lines is C(1,-3).

∴ centre of the given circle is C(1,-3).

Also, the circle passes through the point P(2,4).

∴ radius of the circle

=|CP|=

√

(1-2)2+(-3-4)2

=

√

50

∴ the required equation of the circle is

(x-1)2+(y+3)2=(

√

50

)2

⇒x2+y2-2x+6y-40=0.