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Terminologies Related to a Parabola

Is a Parabola...

Question

Is a Parabola an Ellipse?

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Solution

Checking if a parabola is an ellipse?
An ellipse is a locus of all the points on a plane whose sum of the distance from two fixed points is a constant.
We can consider a parabola as an ellipse with one focal point at infinity.
Therefore, a parabola is an ellipse.

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Q. The equation 16x² + y² + 8xy − 74x − 78y + 212 = 0 represents
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(c) an ellipse
(d) a hyperbola

Q. Mark the correct answer in each of the following:
The negation of the statement "A circle is an ellipse", is
(a) An ellipse is a circle
(b) An ellipse is not a circle
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\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, a > b

and the parabola

x^{2} = 4 (y + b)

are such that the two foci of the ellipse and the end points of the latus rectum of parabola are the vertices of a square. The eccentricity of the ellipse is

What is the difference between identifying a parabola, ellipse, hyperbola, and a circle?

Q. If the vertices of the ellipse

9 x^{2} + 25 y^{2} - 18 x + 100 y - 116 = 0

are the extremities of latus rectum of a parabola whose vertex is

(x_{1}, y_{1})

y_{1} > - 2,

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Terminologies Related to a Parabola

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