Question

10. Find the equation of the circle which passes through the point (2. 4) and centre at the
intersection of the lines x - y = 4 and 2x + 3y + 7 = 0.​

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.