The equation of tangent at `(x_1,y_1)`

The equation of tangent at P(x_(1),y_(1)) to the circle S=0 is given by

Equation of tangent at ' (x_(-)1y_(-)1)

Write the equation of tangent at (1,2) for the curve y=x^(3)+1

Show that the equation of the straight line meeting the circle x^2 + y^2 = a^2 in two points at equal distance d from (x_1, y_1) on the curve is x x_1 + yy_1 - a^2 + 1/2 d^2 = 0 . Deduce the equaiton of the tangent at (x_1, y_1) .

STATEMENT-1 : Tangent at any point P(x_(1), y_(1)) on the hyperbola xy = c^(2) meets the co-ordinate axes at points Q and R, the circumcentre of triangleOQR has co-ordinate (x_(1)y_(1)) . and STATEMENT-2 : Equation of tangent at point (x_(1)y_(1)) to the curve xy = c^(2) is (x)/(x_(1)) + (y)/(y_(1)) =2 .

The equation of the tangents at the origin to the curve y^(2)=x^(2)(1+x) are

The equation of tangent to the curve y=4 xe^(x) at (-1,(-4)/(e )) is

Find the equation of tangent to y=int_(x^(2))^(x^(3))(dt)/(sqrt(1+t^(2))) at x=1

The equation of tangent to the curve y=x^(2)+4x+1 at (-1, -2) is