Binomial Theorem

Question
CBSEENMA11015134

LL' is the latus rectum of a parabola, y2 = 4ax, a > 0. Find the co-ordinates of points L and L'.

Solution

Equation of parabola is y2 = 4ax.
rightwards double arrow   The focus is at S (a, 0).
∴     OS = a
Let coordinates of point L be left parenthesis straight alpha comma space straight beta right parenthesis and of L' bespace space left parenthesis straight alpha comma space minus straight beta right parenthesis with straight beta greater than 0
∴            straight beta squared equals 4 straight a left parenthesis straight a right parenthesis space equals space 4 straight a squared space rightwards double arrow space straight beta space equals space 2 straight a
∴            Coordinates of L are (a, 2a) and of L' are (a, -2a).
                                    

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