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

Asked by Pragya Singh | 11 months ago |  118

Solution :-

The equation is y2 = 10x

Here we know that the coefficient of x is positive.

So, the parabola open towards the right.

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

4a = 10

a = $$\dfrac{10}{4}$$$$\dfrac{5}{2}$$

Thus, co-ordinates of the focus = (a,0) = ($$\dfrac{5}{2}$$, 0)

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

The equation of directrix, x = -a, then,

x = $$- \dfrac{5}{2}$$

Length of latus rectum = 4a = 4($$\dfrac{5}{2}$$) = 10

Answered by Abhisek | 11 months ago

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