True or False:
A line is a normal to a circle if it passes through the centre of the circle.

Find the equation of the circle whose centre is the point (1,-2) and which passes through the centre of the circle x^2 + y^2 + 2y = 3 .

Statement I The line 3x-4y=7 is a diameter of the circle x^(2)+y^(2)-2x+2y-47=0 Statement II Normal of a circle always pass through centre of circle

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

(True/ False) A circle is a plane figure.

A circle cuts two perpendicular lines so that each intercept is of given length. The locus of the centre of the circle is conic whose eccentricity is

Fill in the blanks. The diameter of the circle pass through __

There is one and only one circle passing through three non-collinear points.

Find the equation of the circle whose centre is (2, -3) and which passes through the intersection of the straight lines 3x-2y=1 and 4x+y = 27.