Find the coordinates of the centre, vertices, foci and the equation to the directrices of (i) 2x`^2` + 5y`^` = 10

Find the coordinates of the centre, vertices, foci and the equation to the directrices of (iii) 4x ^1 + 5y ^2 = 1

Find the coordinates of the centre, vertices, foci and the equation to the directrices of (ii) 9x ^2 + 25y ^2 = 225

Find the equation of the directrices of the ellipse x^2/25+y^2/9=1 .

Find the coordinates of vertices,the foci,the eccentricity and the equations of the directrix of the following hyperbola. 16x^2-9y^2=576 .

Find the coordinates of vertices,the foci,the eccentricity and the equations of the directrix of the following hyperbola. x^2/16-y^2/9=1 .

Write the coordinates of the vertex and the focus, the equations of the directrix and the axis, and the length of the latus rectum of the parabola: (i) y ^2 = 16x

Find the equation of the tangent to the curve (ii) x^2 +5y^2 = 9at (2,-1)

Find the eccentricity of the hyperbola (i) x ^2 /4 - y ^2 = 1

Find the equation of the tangent to the curve (iv) y^2 = 4x +5at (1,3)

Find the coordinates of the point R(x, y) which divides the line segment joining the points (i) P(-4, 7) and Q (5, -9) in the ratio 3 : 2 internally.