Find the equation to which the equation `x^2+7x y-2y^2+17 x-26 y-60=0` is transformed if the origin is shifted to the point `(2,-3),` the axes remaining parallel to the original axies.

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+9y^2+14 x+22 y+7=0

Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+8y^2+14 x+22 y+7=0

Find the equation of tangent to the circle x^(2) + y^(2) + 2x -3y -8 = 0 at (2,3)

If theta is the angle between the lines given by the equation 6x^2+5x y-4y^2+7x+13 y-3=0 , then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x-axis.

Find the equation of component lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0 without solving for xor y.

Find the equation of tangents to circle x^(2)+y^(2)-2x+4y-4=0 drawn from point P(2,3).

Find the equation of the normal to y = x^(2) -2x that is parallel to x + 4y -1 = 0

Find the nearest point on the line x - 2y=5 from the origin.

Find the points on the curve x^(2) + y^(2) – 2x – 3 = 0 at which the tangents are parallel to the x-axis.