Find the equation of the tangent to the curve `x^2/a^2-y^2/b^2=1` at the point `(x_1,y_1)`

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

Find the equations of the tangent and the normal to the curve x^2/a^2-y^2/b^2=1 at the point (sqrt2a,b)

Find the equation of the tangent to the curve (X^2)/(a^2) + (y^2)/(b^2) = 1 at (x_0.y_0)

Find the equations of the tangent line to the curve: y = 2x^2 + 3y^2 = 5 at the point (1,1)

Find the equation of the tangent to the ellipse (x^2)/a^2+(y^2)/(b^2) = 1 at (x_1y_1)

if |f(x_1)-f(x_2)|<=(x_1-x_2)^2 Find the equation of tangent to the curve y= f(x) at the point (1, 2).

Find the equation of the tangent to the curve y = -5x^2 + 6x + 7 at the point (1/2 , 35/4)

Find the equations of the tangent and normal to the curve 16x^2 + 9y^2 = 145 at (x_1, y_1) , where x_1=2 and y_1>0 . Also find the points of intersection where both tangent and normal cut the x-axis.