4. x2=-16v

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Solution

The given equation of parabola is x 2 =−16y

Here coefficient of y is negative, hence parabola opens downwards.

General equation of the parabola is given by x 2 =−4ay ,(1)

where ( 0,−a ) represents the coordinates of the focus

Given equation x 2 =−16y can be represented as x 2 =4×4×y (2)

Compare equation (1) and (2),we find that a=4 .

Coordinates of focus is given by ( 0,−a ) (3)

Equation of directrix is given by y=a (4)

Length of latus rectum is given by 4 a (5)

Substitute the value of a in (3), (4) and (5)

Focus= (0,−4)

Equation of directrix is,

y=4 y−4=0

Length of latus rectum =4×4 =16

Since the given equation involves x 2 the axis of the parabola is the y -axis.

Thus the coordinates of focus is ( 0,−4 ) ,axis of parabola is y axis, equation of directrix is y=4 and length of latus rectum is 16.

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Similar questions

In each case, find whether the trinomial is a perfect square or not :

$(i) x^{2} + 14 x + 49$ $(i i) a^{2} - 10 a + 25$

$(i i i) 4 x^{2} + 4 x + 1$ $(i v) 9 b^{2} + 12 b + 16$

$(v) 16 x^{2} - 16 x y + y^{2}$ $(v i) x^{2} - 4 x + 16$

Factorise :

$(i) a^{2} - (b - c)^{2} (i i) 25 (2 x - y)^{2} - 16 (x - 2 y)^{2} (i i i) 16 (5 x + 4)^{2} - 9 (3 x - 2)^{2} (i v) 9 x^{2} - \frac{1}{16} (v) 25 (x - 2 y)^{2} - 4$

If u:v = 2:3, find the ratio 15u + 12v : 20u + 16v

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{(0.99)}^{5} + {(1.01)}^{5}

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