If y = 2x + c is a tangent to the circle x² + y² = 5, then c is __________

The equation of tangent at (1, 2) to the circle x² + y² = 5 is __________

The area of the circle (x - 2)² + (y - k)² = 25 is _________

If (1, -3) is the centre of the circle x² + y² + ax + by + 9 = 0 its radius is _________

The length of the diameter of a circle with centre (1, 2) and passing through (5, 5) is ____________

The auxiliary circle of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 } \) = 1 is __________

The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is ____________

When the eccentricity of a ellipse becomes zero, then it becomes a __________

The distance between the foci of a hyperbola is 16 and e = \(\sqrt { 2 } \). Its equation is ____________

The equation 7x²- 6\(\sqrt { 3 } \) xy + 13y² - 4\(\sqrt { 3 } \) x - 4y - 12 = 0 represents ____________

In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is ________

If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is __________

The length of the latus rectum of the ellipse \(\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 } \) = 1 is __________

The eccentricity of the ellipse 9x²+ 5y² - 30y = 0 is __________

If a parabolic reflector is 20 cm in diameter and 5 cm in diameter and 5 cm deep, then its focus is ____________