Find the equations of, normals to the hyperbola `3x^2-2y^2=10` at points where the line `x + y + 3 = 0` cuts the curve.

Find the eqaution of that normal to the hyperbola 3x^(2)-2y^(2)=10 at points where the line x+y+3=0 cuts the curve.

Find the equtions of tangent and normals to the parabola y^2=4ax at the points where it is cut by the line y=3x-a

Find the equation of the normal to the curve 3x^2-y^2=8 which are parallel to the line x+3y-5=0

Find the equation of normal to the curve, y = .x^3 at the point (2,8).

Find the equation of the normal to the curve y = x^3 at the point (2,1).

Find the equation of normal at point (4, 3) for the hyperbola 3x^(2) - 4y^(2) = 14 .

Find the equation of normal at point (4, 3) for the hyperbola 3x^(2) - 4y^(2) = 14 .

Find the equation of the normal to the hyperbola 3x^(2)-4y^(2)=12 at the point (x_(1),y_(1)) on it. Hence, show that the straight line x+y+7=0 is a normal to the hyperbola. Find the coordinates of the foot of the normal.

Find the equation of the normal lines to the curve 3x^(2)-y^(2)=8 which are parallel to the line x+3y=4 .