Find the equation of the diameter of the circle x`^2` + y`^2` - 14x + 6y + 9 = 0 which passes through the point (2, 1).

Find the equation of the circle concentric with the circle x ^2 + y ^2 - 8x + 12y + 15 = 0 and passing through the point (5, 4).

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

Find the equation of the tangents to the circle x ^2 + y ^2 - 2x - 4y - 4 = 0 which are perpendicular to the line 3x - 4y - 1 = 0

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

Show that x + y = 1 is the equation of the line of a diameter of the circle x ^2 + y ^2 - 4x + 2y + 1 = 0

Find the equations of two tagents to the circle x ^2 + y ^2 = 34 which are parallel to the straight line 5y - 3x + 7 = 0.

Find the equations of the tangents to the hyperbola x ^2 - 2y ^2 = 18 which are perpendicular to the line x - y = 0.

Find the equation of the tanget to the parabola (i) y^2 = 4x which is parllel to 2x + y + 3 = 0

Find the equations of the tangent and the normal to the curve x^ 2 - 4y^2 = 9 at the points (5,-2)