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 tangents to the ellipse 3x ^2 + 4y ^2 = 12 which are perpendicular to the line 2x +y - 4 = 0.

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

Find the equation of the tangent line to the curve y = x^2-2x+7 which is parallel to the 2x -y +9 = 0

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 straight line passing through the point (2, 3) and parallel to the straight line joining the points P(3, -4) and Q(-5, 6).

A straight line passes through the point of intersection of the straight lines 3x - 2y + 4 = 0 and 2x + 3y +5 = 0 and is parallel to the straight line x -y + 5 = 0. Find its equation.

Find the equation of the straight line passing through the point (i) (3, 5) and parallel to the line 4x - 3y + 1 = 0