Conic Sections ...

The length of latus rectum of the ellipse \(3 x^{2}+y^{2}-12 x+2 y+1=0\) is:

Find the equation of the hyperbola, the length of whose latus rectum is 4 and the eccentricity is 3.

The equation \(x^{2}-6 x-3 y+21=0\) represents a/an:

What is the equation of the ellipse having foci \((\pm 2,0)\) and the eccentricity \(\frac{1 }{ 2}\)?

If x = 2 + 3 cos θ and y = 1 - 3 sin θ represent a circle then the centre and radius is:

The number of tangents that can be drawn from \((2,6)\) to \(x^{2}+y^{2}=40\) is:

Equation of the hyperbola whose foci are (5,0) and (-3,0), eccentricity = 2, is:

The equations x = a cos θ - b sin θ , and y = a sin θ + b cos θ, 0 ≤ θ ≤ 2π represent:

Find the equation of directrix of the parabola \(y^{2}+8 y-12 x+4=0 \).

Find the asymptotes to the hyperbola \(9 x^{2}-16 y^{2}=144\).