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Q 01 / 25
The locus of a point whose distance from a fixed point equals its distance from a fixed line is a parabola.
Q 02 / 25
A circle can be considered a special case of a conic section.
Q 03 / 25
The eccentricity of a circle is equal to 1.
Q 04 / 25
The eccentricity of a parabola is always equal to 1.
Q 05 / 25
If the eccentricity of a conic is less than 1, the conic is an ellipse.
Q 06 / 25
The standard equation \(y^2 = 4ax\) represents a parabola opening towards the positive x-axis.
Q 07 / 25
The focus of the parabola \(y^2 = 4ax\) is \((0,a)\).
Q 08 / 25
The directrix of the parabola \(x^2 = 4ay\) is the line \(y = -a\).
Q 09 / 25
In an ellipse, the sum of the distances of any point from the two foci is constant.
Q 10 / 25
The eccentricity of an ellipse can be equal to 1.
Q 11 / 25
The standard equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) represents an ellipse centered at the origin.
Q 12 / 25
If \(a = b\) in the equation of an ellipse, the ellipse becomes a circle.
Q 13 / 25
The distance between the foci of an ellipse is always greater than the length of its major axis.
Q 14 / 25
A hyperbola is defined as the locus of a point for which the difference of distances from two fixed points is constant.
Q 15 / 25
The eccentricity of a hyperbola is always greater than 1.
Q 16 / 25
The equation \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) represents a hyperbola opening along the x-axis.
Q 17 / 25
The asymptotes of a hyperbola intersect at its center.
Q 18 / 25
The eccentricity of a rectangular hyperbola is \(\sqrt{2}\).
Q 19 / 25
The latus rectum of a parabola is always parallel to its directrix.
Q 20 / 25
The length of the latus rectum of the parabola \(y^2 = 4ax\) is \(4a\).
Q 21 / 25
The product of the eccentricities of an ellipse and a hyperbola with the same foci is equal to 1.
Q 22 / 25
In an ellipse, the major axis is always perpendicular to the minor axis.
Q 23 / 25
The director circle of an ellipse exists only when its eccentricity is less than \(\frac{1}{\sqrt{2}}\).
Q 24 / 25
The equation of a tangent to a conic at a point can be obtained by replacing squared terms with product terms.
Q 25 / 25
For a conic section, the eccentricity alone is sufficient to uniquely identify the curve up to similarity.
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