State whether the statements True or False. Justify

The point (1, 2) lies inside the circle x² + y² – 2x + 6y + 1 = 0.

State whether the statements True or False. Justify

The shortest distance from the point (2, –7) to the circle x² + y² – 14x – 10y – 151 = 0 is equal to 5.

State whether the statements True or False. Justify

If the line lx + my = 1 is a tangent to the circle x² + y² = a², then the point (l, m) lies on a circle.

State whether the statements True or False. Justify

The line lx + my + n = 0 will touch the parabola y² = 4ax if ln = am².

State whether the statements True or False. Justify

If P is a point on the ellipse whose foci are S and S′, then PS + PS′ = 8.