Question

The eccentricity of parabola

x2 = −4ay is :​

Answer 1

The eccentricity of the parabola x²=-4ay is 1.

• The eccentricity of the parabola given in standard form is e=1.
• The eccentricity of an ellipse is less than 1 while the eccentricity of a hyperbola is greater tha 1.
• The circle has an eccentricity e =0.
• Eccentricity is a measure of the difference of the figure from a circle, i.e. it shows that how much a figure is different from a circular figure.

Answer 2

SOLUTION

TO DETERMINE

The eccentricity of the parabola

$\sf{ {x}^{2} = - 4ay }$

EVALUATION

The parabola , ellipse and hyperbola have a property in common. Each of them is the locus of a point moving on a plane in such a way that its distances from a fixed point and from a fixed straight line on the plane bear a constant ratio. The fixed point is known as focus , the fixed straight line is the directrix and the constant ratio is eccentricity of the conic . The eccentricity is generally denoted by e

Here the given equation of the parabola is

$\sf{ {x}^{2} = - 4ay}$

So the required eccentricity is 1

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Additional Information :

• For ellipse 0 < e < 1

• For hyperbola e > 1

• These names are due to Appollonius ( 3rd century B.C )

• They have been defined as locii of a moving point by Pappus of Alexandria ( 300 A.D ).

• Descartes showed that their equations are of second degree

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