List of top Mathematics Questions on Conic sections asked in KEAM

Axis of parabola is \( x = 0 \). If the vertex is at a distance of 3 from the origin above the x-axis, find the vertex.
Equation of parabola having focii (-3, 1) and (3, 1)
Suppose a and b are lengths of major and minor axes of an ellipse that passes through the points (4,3) and (-1,4). If the major axis of the ellipse lies along the x-axis , then the value of \(\frac{1}{a^2}+\frac{16}{b^2}\) is
The end points of the major axis of an ellipse are (2, 4) and (2,-8). If the distance between foci of this ellipse is 4, then the equation of the ellipse is
The eccentricity of the hyperbola \(\frac{(x-3)^2}{9}+\frac{4(y-1)^2}{45}=1\) is equal to
If (-1, 0) and (3, 0) are foci of an ellipse and the length of the major axis is 6, then the length of the minor axis is
The centre of the ellipse x2+7y2-14x+28y+49=0 is
If the line 2x-3y+c=0 passes through the focus of the parabola x2 = -8y, then the value of c is equal to
The foci of a hyperbola are (8, 3) and (0, 3) and eccentricity is \(\frac{4}{3}\). Then the length of the transverse axis is
One of the vertices of the major axis of an ellipse is (1, 1) and one of the vertices of its minor axis is (-2, -1). If the centre of the ellipse is (-2, 1), then the equation of the ellipse is
Distance between two foci of the hyperbola \( x^2 - 4y^2 = 16 \) is