Conic Sections ...

Find the radius of the circle, \(5 x^{2}+5 y^{2}-20 x-6 y+15=0\).

A tangent touches the parabola y² = -8x at the point (-2, 4) then the slope of the tangent is:

The second degree equation \(2 x^{2}+2 y^{2}-5 x-7 y-3=0\) represents:

Find the length of the conjugate axis of the hyperbola \(\frac{y^{2}}{16}-\frac{x^{2}}{49}=1\).

The equation of the hyperbola, whose centre is at the origin \((0,0)\), foci \((\pm 3,0)\) and eccentricity \(e=\frac{3}{2}\):

The equation of a circle with diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area of 154 sq. units is:

Find the equation of a circle touching both the x-axis and y-axis and has centre at (-2, -2).

Find the equation of the circle whose end points of the diameter are (- 3, 5) and (5, 3).

Find the equation of the parabola with vertex at the origin, the axis along the x-axis and passing through the point P(3, 4).

If the line \(x-1=0\) is the directrix of the parabola \(y^{2}-k x+8=0\), then one of the values of \(k\) is: