NCERT Solutions Class 11 Maths Chapter 11: Conic Sections

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NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections are provided in the article. Conic section is a curve formed by intersecting a plane with a cone. The curves that are formed are Circles, Ellipse, Parabola, and Hyperbola.

Download: NCERT Solutions for Class 11 Mathematics Chapter 11 pdf

Class 11 Maths NCERT Solutions Chapter 11 Conic Sectios

Class 11 Maths NCERT Solutions Chapter 11 Conic Sections are provided below:

Also read: Concept Notes on Conic Sections

Important Topics: Class 11 Maths NCERT Solutions Chapter 11 Conic Sections

Important Topics Class 11 Maths NCERT Solutions Chapter 11 Conic Sections are elaborated below:

Sections of a Cone

There are three sections of a cone or conic sections: Parabola, Hyperbola, and Ellipse (Circle is a special kind of Ellipse).

Circle

Circle is the simplest conic section. As a conic section, circle is intersection of a plane perpendicular to the cone's axis.

Please Note:

Value of eccentricity(e) for a circle is e = 0.

Circle has no directrix.

General form of the equation of a circle with center at (h, k), and radius r: (x−h)² + (y−k)² = r²

Parabola

When intersecting plane is at an angle to the surface of the cone, thwe obtained conic section is called the parabola. It is a U-shaped conic section.

The value of eccentricity(e) for parabola is e = 1

Ellipse

Ellipse is a conic section that is formed when plane intersects with cone at an angle. Ellipse has 2 foci, a major axis, as well as a minor axis.

Please Note:

Value of eccentricity(e) for ellipse is e < 1.
Ellipse has 2 directrices.
The conic section formula for an ellipse is: (x−h)²/a² + (y−k)²/b² = 1

Hyperbola

Hyperbola is formed when interesting plane is parallel to axis of the cone, and intersect with both nappes of the double cone.

General form of equation of hyperbola with (h, k) as the center is:

(x−h)²/a² - (y−k)²/b² = 1

NCERT Solutions For Class 11 Maths Chapter 11 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 11 Conic Sections under different exercises are as follows:

Also check:

Chapter Related Topics
Eccentricity of Ellipse	Latus rectum of Ellipse	Parabola Formula
Latus rectum of Hyperbola	Eccentricity	Locus

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

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2.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).

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3.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

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4.
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i) target is hit.
(ii) at least one shot misses the target.

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5.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.

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6.
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions:

(i) What is the probability that selected person is a female?
(ii) If a male person is selected, what is the probability that he will not be suffering from lung problems?
(iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female.
OR
(iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male.

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NCERT Solutions For Class 11 Maths Chapter 11: Conic Sections

Class 11 Maths NCERT Solutions Chapter 11 Conic Sectios

Important Topics: Class 11 Maths NCERT Solutions Chapter 11 Conic Sections

NCERT Solutions For Class 11 Maths Chapter 11 Exercises:

CBSE CLASS XII Related Questions

1.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

3.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

Similar Mathematics Concepts

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NCERT Solutions For Class 11 Maths Chapter 11: Conic Sections

Class 11 Maths NCERT Solutions Chapter 11 Conic Sectios

Important Topics: Class 11 Maths NCERT Solutions Chapter 11 Conic Sections

NCERT Solutions For Class 11 Maths Chapter 11 Exercises:

CBSE CLASS XII Related Questions

1.Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

3.Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]

3.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).