The curve formed when a slightly tilted plane cuts only one nappe of the cone is
The curve formed when a plane, perpendicular to the axis of the cone, intersects it at any point other than vertex, is
The curve formed when a plan parallel to generator, of the cone, intersects its one nappe only is
The centre and radius of the circle 2x + 6y − x² − y² = 1 are:
The equation of the circle with centre (4, −2) and radius 8 units is:
The equation of the circle passing through the points (1, 4), (7, 5), and (1, 8) is:
For the general equation ax² + by² + 2hxy + 2gx + 2fy + c = 0, the condition for it to represent a circle is:
The equation of the circle with centre at the origin and radius 10 units is:
The equation of the circle passing through (4, 5) with centre at (2, 2) is:
The equation of the circle passing through the points (1, −2) and (3, −4) and touching the x-axis is:
The equation of the circle passing through the points (1, 4), (7, 5), and (1, 8) is:
The equation of the circle that passes through the point (−2, −4) and has the same centre as the circle x² + y² − 4x − 6y − 23 = 0 is:
The equation of the circle that touches the x-axis and passes through the points (1, −2) and (3, −4) is:
The equation of a circle passing through (−1, −2) and concentric with the circle x² + y² − 3x + 4y + c = 0 is:
Which of the following loci always passes through the fixed points (a, 0) and (−a, 0)?
The equation of the circle that passes through the origin and cuts off intercepts 3 and 4 on the axes is:
Under which one of the following conditions does the circle x² + y² + 2gx + 2fy + c = 0 meet the x-axis in two points on opposite sides of the origin?
The centre of the circle (x − α)² + (y − β)² = 9 lies on the line x = y, and the circle touches the circle x² + y² = 1 externally. The values of α and β are:
A circle lies in the first quadrant and touches the x-axis at (3, 0) and the y-axis at (0, 3). Its equation is:
Find the equation of the circle whose centre lies on the line x = 1 − y, and which passes through the points (0, 0) and (4, 2).
