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NCERT Solutions for Class 11 Math Ch-10: Conic Sections
NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections covers the standard equations and properties of circles, parabolas, ellipses, and hyperbolas formed by the intersection of a plane with a double-napped cone.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What is the standard equation of a circle with centre (h, k) and radius r?
Answer: The standard equation of a circle with centre (h, k) and radius r is given by (x − h)² + (y − k)² = r². When the centre is at the origin, this simplifies to x² + y² = r².
Q2: What is the standard equation of a parabola that opens to the right, and what is its latus rectum?
Answer: The standard equation of a rightward-opening parabola with vertex at the origin is y² = 4ax, where a > 0. Its latus rectum (the chord through the focus perpendicular to the axis) has a length of 4a.
Q3: What is the standard equation of an ellipse, and how is its eccentricity defined?
Answer: The standard equation of an ellipse with the major axis along the x-axis is x²/a² + y²/b² = 1, where a > b. Its eccentricity is defined as e = c/a, where c² = a² − b², and it measures how much the ellipse deviates from being circular (0 < e < 1).
Q4: What is the standard equation of a hyperbola, and what is its eccentricity range?
Answer: The standard equation of a hyperbola with the transverse axis along the x-axis is x²/a² − y²/b² = 1. Its eccentricity is given by e = c/a, where c² = a² + b², and for a hyperbola, the eccentricity is always greater than 1 (e > 1).
Q5: How does a conic section's type depend on the angle at which a plane intersects a double-napped cone?
Answer: A circle is formed when the plane is perpendicular to the axis of the cone; an ellipse is formed when the plane cuts one nappe at an angle to the axis but not parallel to a generator; a parabola is formed when the plane is parallel to a generator of the cone; and a hyperbola is formed when the plane cuts through both nappes of the cone.
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