The locus of the point of intersection of perpendicular tangents of the parabola y² = 4ax is

Th point of curve y = 2x² - 6x - 4 at which the targent is parallel to x - axis is __________

The locus of the point of Intersection of perpendicular tangents to the hyperbela \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } \) = 1 is __________

The tangent at any point P on the ellipse \(\frac { { x }^{ 2 } }{ 6 } +\frac { { y }^{ 2 } }{ 3 } \) = 1 whose centre C meets the major axis at T and PN is the perpendicular to the major axis; The CN CT = ______________

The length of major and minor axes of 4x² + 3y² = 12 are ____________

If B, B¹ are the ends of minor axis, F₁, F₂ are foci of the ellipse \(\frac { { x }^{ 2 } }{ 8 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 then area of F₁BF₂B¹ is __________

The point of contact of y² = 4ax and the tangent y = mx + c is _________

The number of normals to the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 from an external point is ________

In an ellipse 5x² + 7y² = 11, the point (4, -3) lies _________ the ellipse

The angle between the tangents drawn from (1, 4) to the parabola y² = 4x is __________

The line y = mx +1 is a tangent to the parabola y² = 4x if m = ______________

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 __________

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 __________

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 ________

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 ____________

Equation of tangent at (-4, -4) on x² = -4y is _____________

The equation of the directrix of the parabola y²+ 4y + 4x + 2 = 0 is ___________