For three consecutive odd integers $a, b$ and $c$,if the variable line $a x+b y+c=0$ always passes through the point $(\alpha, \beta)$,the value of $\alpha^2+\beta^2$ equals

$A$ variable line passes through a fixed point $P$. If the algebraic sum of the perpendiculars drawn from $(2, 0)$,$(0, 2)$,and $(1, 1)$ to the line is zero,then the coordinates of the point $P$ are:

$A$ straight line $L$ with negative slope passes through the point $(1,1)$ and cuts the positive coordinate axes at the points $A$ and $B$. If $O$ is the origin,then the minimum value of $OA + OB$ as $L$ varies,is

Let $A(2, 3)$ and $B(-4, 5)$ be two fixed points. If a point $P(x, y)$ moves such that the area of $\Delta PAB = 12$ square units,find the locus of $P$.

The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

Let $A(5, -3)$,$B(3, -2)$,and $C(-1, 5)$ be three points. If $P$ is a point satisfying the condition $PA^2 + 2PB^2 = 3PC^2$,then a point that lies on the locus of $P$ is