The point of concurrence of all conjugate lines of the line $5x + 7y - 78 = 0$ with respect to the circle $x^2 + y^2 + 6x + 8y - 96 = 0$ is

The equation of the polar of $(1, 1)$ with respect to the circle $x^2+y^2+4x+6y-3=0$ is

The locus of the poles of normal chords of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by:

Consider the point $P(\alpha, \beta)$ on the line $2x+y=1$. If $P$ and $(3,2)$ are conjugate points with respect to the circle $x^2+y^2=4$,then $\alpha+\beta=$

Consider the circles $S_1: x^2+y^2+2x+8y-23=0$ and $S_2: x^2+y^2-4x+10y+19=0$. If the polars of the centre of one circle with respect to the other circle are $L_1$ and $L_2$,then $L_1$ and $L_2$ are

The inverse of the point $(1, 2)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$ is