Question

The image of origin about the line 3x + 5y = 17 is
(1) (3,5)
(2) (-2,8)
(3) (2, 28/5)
(4) (4, 22/5)​

Answer 1

Given equation of circle:-

x2+y2+4x+6y+9=0

Given equation of line:-

3x+5y+17=0.....(1)

Let P(a,b) be the pole of line 3xx+5y+17=0 w.r.t. the circle x2+y2+4x+6y+9=0

Now equation of polar of point P(a,b) w.r.t. the circle x2+y2+4x+6y+9=0-

ax+by+2(x+a)+3(y+b)+9=0

⇒(a+2)x+(b+3)y+(2a+3b+9)=0.....(2)

As the equation (2)&(3) are same, therefore,

3a+2=5b+3=172a+3b+9

Now,

Case I:-

3a+2=5b+3

⇒5(a+2)=3(b+3)

⇒5a