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Translated Parabola Symmetric about a Line Parallel to x- axis

The eccentric...

Question

The eccentricity will increase when a standard parabola $y^{2} = 4 a x$ is translated along both the axes.

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Q. The axis of parabola

y^{2} = 4 a x

gets shifted when a parabola is translated vertically.

Q. The equation of the parabola

y^{2} = 4 a x

when it is translated horizontally to point

(h, 0)

Q. Determine the differential equation of parabolas with foci at origin and axes along X-axis.
Hint:

y^{2} = 4 a (x - a)

y^{2} = 16 x

translated to the coordinates

(1, 4) .

If the equation of translated parabola is

y^{2} + a x + b y + c = 0.

Find the value of

(a + b + c)

.

Q. When a standard parabola

y^{2} = 4 a x

is flipped about y-axis, then what will be the equation of directrix and coordinates of focus of new parabola?

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