Class 11 • Maths • Chapter 10
CONIC SECTIONS
True & False Quiz
Slice the cone. Reveal the curve.
✓True
✗False
25
Questions
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Ch.10
Chapter
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XI
Class
Why True & False for CONIC SECTIONS?
How this format sharpens your conceptual clarity
🔵 Conics describe planetary orbits (ellipse), projectile paths (parabola), and satellite dishes — they are nature's curves.
✅ T/F tests standard equations, eccentricity values, and focus-directrix relationships — CBSE Board staples.
🎯 Eccentricity: circle e=0, ellipse 0<e<1, parabola e=1, hyperbola e>1 — most-tested classification.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The locus of a point whose distance from a fixed point equals its distance from a fixed line is a parabola.
Q 2
A circle can be considered a special case of a conic section.
Q 3
The eccentricity of a circle is equal to 1.
Q 4
The eccentricity of a parabola is always equal to 1.
Q 5
If the eccentricity of a conic is less than 1, the conic is an ellipse.
Q 6
The standard equation \(y^2 = 4ax\) represents a parabola opening towards the positive x-axis.
Q 7
The focus of the parabola \(y^2 = 4ax\) is \((0,a)\).
Q 8
The directrix of the parabola \(x^2 = 4ay\) is the line \(y = -a\).
Q 9
In an ellipse, the sum of the distances of any point from the two foci is constant.
Q 10
The eccentricity of an ellipse can be equal to 1.
Q 11
The standard equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) represents an ellipse centered at the origin.
Q 12
If \(a = b\) in the equation of an ellipse, the ellipse becomes a circle.
Q 13
The distance between the foci of an ellipse is always greater than the length of its major axis.
Q 14
A hyperbola is defined as the locus of a point for which the difference of distances from two fixed points is constant.
Q 15
The eccentricity of a hyperbola is always greater than 1.
Q 16
The equation \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) represents a hyperbola opening along the x-axis.
Q 17
The asymptotes of a hyperbola intersect at its center.
Q 18
The eccentricity of a rectangular hyperbola is \(\sqrt{2}\).
Q 19
The latus rectum of a parabola is always parallel to its directrix.
Q 20
The length of the latus rectum of the parabola \(y^2 = 4ax\) is \(4a\).
Q 21
The product of the eccentricities of an ellipse and a hyperbola with the same foci is equal to 1.
Q 22
In an ellipse, the major axis is always perpendicular to the minor axis.
Q 23
The director circle of an ellipse exists only when its eccentricity is less than \(\frac{1}{\sqrt{2}}\).
Q 24
The equation of a tangent to a conic at a point can be obtained by replacing squared terms with product terms.
Q 25
For a conic section, the eccentricity alone is sufficient to uniquely identify the curve up to similarity.
Key Takeaways — CONIC SECTIONS
Core facts for CBSE Boards & JEE
1
e=0 (circle); 0<e<1 (ellipse); e=1 (parabola); e>1 (hyperbola).
2
Circle: (x−h)²+(y−k)²=r²; centre (h,k), radius r.
3
Ellipse x²/a²+y²/b²=1 (a>b): c²=a²−b², foci at (±c,0).
4
Parabola y²=4ax: focus (a,0), directrix x=−a, latus rectum=4a.
5
Hyperbola x²/a²−y²/b²=1: c²=a²+b² (NOT minus).
6
A circle is a special ellipse where a=b=r; eccentricity becomes 0.