The circle x²+y²+2gx+2fy+c = 0 does not intersect x − axis if ______.

The difference between the lengths of the major axis and the latus rectum of an ellipse is ______.

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is _______.

The difference of the focal distances of any point on the hyperbola is equal to ______.

The latus rectum of the hyperbola \({ 16x }^{ 2 }-{ ay }^{ 2 }=144\quad is\) _______.

Find the equation of the parabola which is symmetric about the Y-axis and psses through the point (2,-3).

Find the equation of the parabola with vertex at the borigin, the axis along the X-axis and passing through the point (2, 3)

Find the centre and radius of each of the following circles:
2x²+2y²-4x-8y-17=0

Find the centre and radius of each of the following circles:
4x²+4y²-10x+5y+5=0

Find the equation of a circle touching both the axis and passing through the point (6, 3).

Find the equation of circle whose center is(1, 2) and touches X-axis

Find the equation of a circle whose center is(2,0) and touches Y-axis.

Find the equation of the circle whose radius is 5 and which touches the circule x²+y²−2x−4y−20=0 externally at the point (3,7).

Find the equation of the ellipse whose focus is(1,-1), the directrix is the line x-y-3=0 and eccentricity is 1/2.

Find the foci,vertices, eccentricity and length of latusrectum of the hyperbola \(5{ y }^{ 2 }+{ 9x }^{ 2 }=36\)

Find the area of the triangle formed by the lines joining the vertex of the parabola \({ x }^{ 2 }=12y\) to the ends of its latusrectum.

The foci of a hyperbola coincide with the faci of the elipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\) find the equation of the hyperbola if its eccentricity is 2.

Find the equation of the hyperbola satisfying the given conditions.
Foci (0, ± \(\sqrt10\) ),passing through (2, 3)

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

Find the equation of the parabola whose vertex is at (2,1) and the directrix x = y = 1