Question

The polar of (2,3) with respect to the circle x^2+y^2-4x-6y+2=0 is?​

Answer 1

Step-by-step explanation:

The polar of the general equation of circle w.r.t point (x

1

,y

1

) is

xx

1

+yy

1

+g(x+x

1

)+f(y+y

1

)+c=0

Then, the polar of the general equation of given circle w.r.t point (−2,3) is

⇒x(−2)+y(3)−2(x−2)−3(y+3)+5=0

⇒−4x+0+4−9+5=0

Equation of polar is x=0

Answer 2

Answer:

The polar of $(2,3)$ with respect to the circle $x^2+y^2-4x-6y+2=0$ ​does not exist

Step-by-step explanation:

Given: Point $(2,3)$ and equation of the circle is $x$² $+$ $y$²$-4x-6y+2=0$

To find: The polar$(2,3)$ w.r.t.the circle.

Solution:

Circle $x^2+y^2-4x-6y+2=0$ compare with $x^2+y^2+2gx+2fy+c=0$

$g=-2,f=-3,c=2$

The polar of the general equation of circle is w.r.t. point $x$₁ , $y$₁ is

$xx$₁ + $yy$₁ + $g(x+x$₁$)+f(y+y$₁$)+c=0$

Then, the polar of the general equation of the given circle w.r.t. point$(2,3)$ is

$x$ × $2$ + $y$ × $3$ $-2(x+2)$$-3(y+3)+2=0$

$2x+3y-2x-4-3y-9+2=0$

$-11\neq 0$

Hence, the polar does not exist.