Is The equation of tangent yy1 = 2a(X+x1) at (x1, y1) is valid only for y square = 4ax or valid for all parabolas?

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The equation of the tangent at $(x_{1}, y_{1})$ to a curve $y^{2} = 4 a x$ at a point $(x_{1}, y_{1})$ is given by $y y_{1} = 2 a (x + x_{1})$

Q. For the circle

(x - h)^{2} + (y - k)^{2} = a^{2}

, the equation of the tangent at point

(x_{1}, y_{1})

is given by

(x_{1} - h) (x - x_{1}) + (y_{1} - k) (y - y_{1}) = 0

The equation of tangent to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ at its point $(x_{1}, y_{1})$ is given by $x x_{1} + y y_{1} + g (x + x_{1}) + f (y + y_{1}) + c = 0$

The equation of the chord of the circle $x^{2} + y^{2} = a^{2}$ having $(x_{1}, y_{1})$ as its mid-point is

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