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CLASS 11 MATHEMATICS • CHAPTER 10

Conic Sections – Online Practice Worksheet

Master Circle, Parabola, Ellipse & Hyperbola with randomized questions, instant feedback and complete chapter revision.

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📚 Complete Conic Sections Class 11 Practice Guide

Conic sections are important curves in coordinate geometry. The principal conics are the circle, parabola, ellipse and hyperbola. This worksheet organizes practice around these chapter parts and provides repeated numerical and conceptual revision. The NCERT link supplied for this worksheet is the official NCERT Textbooks PDF access page. citeturn0view0

1. Circle

A circle is the locus of a point at a fixed distance from a fixed point. The fixed point is the centre and the fixed distance is the radius.

📌 Centre (0,0): x²+y²=r²
📌 Centre (h,k): (x−h)²+(y−k)²=r²

Read the signs inside the brackets carefully. In an expanded equation, completing the square can recover the centre and radius.

2. General Equation of a Circle

⭐ x²+y²+2gx+2fy+c=0

Centre = (−g,−f) and radius = √(g²+f²−c) when the radius is real.

3. Parabola

A parabola is the locus of a point whose distance from a fixed focus equals its perpendicular distance from a fixed directrix.

📌 y²=4ax → focus (a,0), directrix x=−a
📌 y²=−4ax → focus (−a,0), directrix x=a
📌 x²=4ay → focus (0,a), directrix y=−a
📌 x²=−4ay → focus (0,−a), directrix y=a
📌 Latus rectum length = 4a

Always compare the displayed coefficient with 4a. If y²=20x, then a=5, not 20.

4. Ellipse

An ellipse is a closed conic with two foci. For a horizontal standard ellipse:

📌 x²/a²+y²/b²=1, a>b
📌 c²=a²−b²
📌 e=c/a, 0<e<1

The major and minor axes have lengths 2a and 2b. The foci are (±c,0) for the horizontal form. If the larger denominator is under y², the major axis is vertical.

📌 Ellipse latus rectum = 2b²/a

5. Hyperbola

A hyperbola has two branches. For a horizontal standard hyperbola:

📌 x²/a²−y²/b²=1
📌 c²=a²+b²
📌 e=c/a>1

The vertices are (±a,0), foci are (±c,0), and the asymptotes are:

⭐ y=±(b/a)x
📌 Hyperbola latus rectum = 2b²/a

6. Eccentricity

⭐ Circle: e=0   Ellipse: 0<e<1   Parabola: e=1   Hyperbola: e>1

Eccentricity is a useful classification tool and can also help check whether a calculated answer is reasonable.

7. Practice Question Types & Sub-Parts

The tool covers circle centre, circle radius, general circle, parabola parameter, focus, directrix and latus rectum, ellipse focal distance, eccentricity, major axis and latus rectum, hyperbola focal distance, eccentricity, asymptote slope and latus rectum, plus conic identification. Each question includes a related sub-part or formula hint.

8. Exam Strategy

  1. Identify the conic and compare the equation with standard form.
  2. Write down a, b, c or r before calculating.
  3. For a parabola, remember the coefficient is 4a.
  4. For an ellipse use c²=a²−b².
  5. For a hyperbola use c²=a²+b².
  6. Use e=c/a for ellipse and hyperbola.
  7. Check signs, orientation and units of the requested quantity.

9. Common Mistakes

Do not read centre signs incorrectly. Do not mistake 4a for a. Do not interchange the ellipse and hyperbola formulas for c². Do not use a/c for eccentricity. For focus and directrix, first determine the opening direction.

10. How to Use This DigiSadhan Worksheet

Select questions, mode, chapter part, difficulty and optional timer, then press Start New Test. Answer each question and click Check Answer. Correct input becomes green and incorrect input becomes red. Show Answer stays locked until checking. MCQ options are independently shuffled. The progress bar, score and accuracy update live. Sound can be turned off. Shuffle creates a fresh randomized worksheet while keeping the selected settings.

11. Complete Revision After the Test

After completing a test, use the formula boxes above to review the chapter. For circles, revise centre and radius. For parabolas, revise 4a, focus, directrix and latus rectum. For ellipses, revise a, b, c and eccentricity. For hyperbolas, revise c²=a²+b² and asymptotes. Then generate another fresh test. Repeated practice—attempt, check, review, retry—builds confidence and calculation speed across the complete Conic Sections chapter.

12. Final Checklist

Before an examination, make sure you can identify each conic from its standard equation, calculate its main parameters, distinguish ellipse from hyperbola, locate a parabola's focus and directrix, and use eccentricity correctly. Practise both objective and short-answer questions so that formula recall and application become automatic.