If one end of a focal chord AB of the parabola y2 = 8x is at [A( 1 2, - 2 )], then the equ…

Question

If one end of a focal chord AB of the parabola
y2 = 8x is at $$A\left( {{1 \over 2}, - 2} \right)$$, then the equation of
the tangent to it at B is :

Accepted Answer

Given parabola y2
 = 8x

$$ \therefore $$ a = 2

Let one end of focal chord is A(at2
, 2at) = $$\left( {{1 \over 2}, - 2} \right)$$

$$ \therefore $$ 2at = -2

$$ \Rightarrow $$ t = $$ - {1 \over 2}$$

Other end of focal chord will be B$$\left( {{a \over {{t^2}}}, - {{2a} \over t}} \right)$$ $$ \equiv $$ (8, 8)

$$ \therefore $$ Equation of tangent at B is

8y = 4(x + 8)

$$ \Rightarrow $$ x -- 2y + 8 = 0

Solutions · 1