Question

find the length of focal chord of slope 2 of parabola y^=4x(urgent)

Answer 1

the length of focal chord of slope 2 of parabola y² = 4x is 5 units

Step-by-step explanation:

We know that for parabola $y^2=4ax$, the focus is at $(a,0)$

Therefore, for the given parabola $y^2=4x$, the focus will be at $(1,0)$

The equation of the focal chord will be the equation of the line passing through (1, 0) and having a slope of 2

Therefore, the equation of the focal chord

$(y-0)=2(x-1)$

$\implies y=2x-2$

Here m = 2 and c = -2

We know that length of $y=mx+c$ on $y^2=4ax$ is given by

$\frac{4}{m^2}\sqrt{a(1+m^2)(a-mc)}$

Here, a = 1, m = 2, c = -2

Thus, the length of the focal chord

$=\frac{4}{2^2}\sqrt{1(1+2^2)(1-2\times(-2))}$

$=\frac{4}{4}\sqrt{5\times5}$

$=5$

Thus, the length of focal chord is 5 units

Hope this answer is helpful.

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Answer 2

Answer:

Here is your answer:-

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