Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 10x

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Solution

The given equation is y² = 10x.

Here, the coefficient of x is positive. Hence, the parabola opens towards the right.

On comparing this equation with y²= 4ax, we obtain

∴Coordinates of the focus = (a, 0)

Since the given equation involves y², the axis of the parabola is the x-axis.

Equation of directrix,

Length of latus rectum = 4a = 10

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