If one end of a focal chord AB of the parabola y^{2}=8x is at A\left ( \frac{1}{2},-2 \right ), then the equation of the tangent to it at B is :
Option: 1 x+2y+8=0
Option: 2 2x-y-24=0
Option: 3 x-2y+8=0
Option: 4 2x+y-24=0
 

Answers (1)

 

 

Length of the Latus rectum and parametric form -

Parametric Equation:

From the equation of the parabola, we can write 
\\\frac{y}{2a}=\frac{2x}{y}=t\text{ here, t is a parametewr}\\\\\text{Then, }x=at^2 \text{ and }y=2at\text{ are called the parametric equations }\\\text{and the point } (at^2,2at)\text{ lies on the parabola.}

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Tangents of Parabola in Point Form -

Tangents of Parabola in  Point Form

\\ {\text { Equation of the tangent to the parabola } \mathrm{y}^{2}=4 \mathrm{ax} \text { at the point } \mathrm{P}\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { is }} \\ {\mathrm{y} \mathrm{y}_{1}=2 \mathrm{a}\left(\mathrm{x}+\mathrm{x}_{1}\right)}

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y^{2}=8 x \text { then } A\left(2 t_{1}^{2}, 4 t_1\right) \\ {\text { given } A\left(\frac{1}{2},-2\right) \Rightarrow t_{1}=-1 / 2}

t_1\cdot t_2=-1

\text { then } t_{2}=2 \Rightarrow B(8,8) \\ \text { Equation of tangent } 8 y=4(x+8) \\ {2 y=x+8}

Correct Option 3

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