True or False:
The point (1,2) lies inside the circle `x^2 + y^2 - 2x + 6y +1 = 0`.

If the point (1, 4) lies inside the circle x^(2)+y^(2)-6x-10y+p=0 then p is:

A circle passes through point (3, sqrt(7/2)) and touches the line-pair x^2 - y^2 - 2x +1 = 0 . Centre of circle lies inside the circle x^2 + y^2 - 8x + 10y + 15 = 0 . Coordinates of centre of circle are given by

If the points (lambda, -lambda) lies inside the circle x^2 + y^2 - 4x + 2y -8=0 , then find the range of lambda .

State True/False: The point (1,2) satisfies 2x + y ge 5

True or false The line x=y=z lies in the plane x-2y+z-1=0.

Find the equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0, x^2 + y^2 + 2x - 4y -6 = 0 and with its centre on the line y = x.

The point diametrically opposite to the point P(1, 0) on the circle x^(2)+y^(2) + 2x+4y- 3 = 0 is

Find the equation of a circle, which touches the line x+ y = 5 at the point (-2, 7) and cuts the circle x^2+ y^2+ 4x - 6y +9 =0 orthogonally.

The point ([p+1], [p]) is lying inside the circle x^2+y^2-2x-15=0 and x^2+y^2-2x-7=0 . Then the set of all values of p is (where [.] represents the greatest integer function)

If lx+my=1 touches the circle x^(2)+y^(2)=a^(2) , prove that the point (l,m) lies on the circle x^(2)+y^(2)=a^(-2)