Given the parabola $y^{2} = 4 a x$ , the general form of tangent at point $(x^{'}, y^{'})$ can be given by $T^{2} = S S^{'}$ Where, $T = y y^{'} - 2 a (x + x^{'}), S = y^{2} - 4 a x, S^{'} = y^{'} 2 - 4 a x^{'}$

True

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False

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Solution

The correct option is A
True

The equation of a pair of tangents to any second degree curve

$S = a x^{2} + 2 h x y + b y^{2} + 2 a x + 2 f y + c = 0$

is given by $S S_{1} = T^{2},$

where $S_{1} = a {x_{1}}^{2} + 2 h x_{1} y_{1} + b {y_{1}}^{2} + 29 x_{1} + 2 f y_{1} + c$

T is obtained by replacing x by $\frac{x + x_{1}}{2} y$ by $\frac{y + y_{1}}{2}, x^{2}$ by $x x_{1}, y^{2}$ by $y y,$ and $x y$ by $\frac{x y_{1} + y x_{1}}{2} .$

Therefore the option is true

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Given the parabola y2=4ax, the general form of tangent at point (x′,y′) can be given by T2 = SS′ Where, T = yy′ − 2a (x + x′), S =y2 − 4ax,S′ = y′2 − 4ax′

Given the parabola $y^{2} = 4 a x$ , the general form of tangent at point $(x^{'}, y^{'})$ can be given by $T^{2} = S S^{'}$ Where, $T = y y^{'} - 2 a (x + x^{'}), S = y^{2} - 4 a x, S^{'} = y^{'} 2 - 4 a x^{'}$