A chord BC is drawn in a parabola $y^{2} = 4 x$ such that x cordinate of C is twice that of B. Also OB makes $45^{\circ}$ with x-axis. What is the projecton of BC on y-axis?

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Solution

Given parabola is,

$y^{2} = 4 x$

$B \equiv (x, x) (s i n c e s l o p e o f O B i s 1)$

X coordinate of C=2 times x coordinate of B.

$C \equiv (2 x, y)$

Since (x,x) lies on the parabola $y^{2} = 4 x$ ,

$x^{2} = 4 x$

$\Rightarrow x = 4$

i.e., $B \equiv (4, 4)$

$C \equiv (8, y_{1})$

$∴$ projection of BC on x-axis $= X_{C} - X_{B}$

$= 4$

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