1. Permutation and Combination
    2. 1. Introduction (1.1)
    2. Permutation (1.2)
    3. Combination (1.3)
  2. Binomial Theorem, Exponential and Logarithmic Series
    3. 4. Binomial theorem (2.1)
    5. Application of Binomial series (2.2)
    6. Exponential and Logarithmic series (2.3)
  3. Complex Nunber
    4. 7. (3.1)
    8. (3.2)
  4. Sequence and Series
    5. 9. (4.1)
    10. Principle of Mathematical Induction (4.2)
  5. Matrix based System of Linear Equations
    6. 11. (5.1)
    12. (5.2)
    13. (5.3)
    14. (5.4)
  6. Properties of Triangle
    7. 15. (6.1)
  7. Solution of Triangle
    8. 16. (7.1)
  8. Conic Section
    9. 17. Circle (8.1)
    18. Parabola (8.2)
    19. Tangents and Normal of Parabola (8.3)
    20. Ellipse and its Standard Equation (8.4)
    21. Hyperbola (8.5)
  9. Product of Vectors Vectors
    10. 22. (9.1)
    23. (9.2)
  10. Correlation and Regression Analysis
    11. 24. (10.1)
    25. (10.2)
    26. (10.3)
  11. Probability
    12. 27. (11.1)
  12. Derivatives
    13. 28. Limit, Continuity and Derivative
    29. Derivatives of Hyperbolic Functions (12.1)
  13. Applications of Derivatives
    14. 30. (13.1)
    31. (13.2)
    32. (13.3)
    33. (13.4)
  14. Antiderivative
    15. 34. (14.1)
    35. (14.2)
    36. (14.3)
    37. (14.4)
  15. Differential Equations
    16. 38. (15.1)
    39. (15.2)
    40. (15.3)
    41. (15.4)
    42. (15.5)
  16. System of Linear Equations
    17. 43. (16.1)
    44. (16.2)
  17. Linear programming
    18. 45. (17.1)
  18. Statics
    19. 46. (18.1)
  19. Dynamics: Newton's Laws of Motion and Projectile
    20. 47. (19.1)
    48. (19.2)
    49. (19.3)
    50. (19.4)
Conic Section
17. Circle (8.1)

Question Answers

Q.

Find the equations of tangents and normals to the following circles

  1. \(x^2+y^2=8\) at (2, 2)
  2. \(x^2+y^2=36\) at (-6, 0)
  3. \(x^2+y^2-6x-8y-4=0\) at (8, 6)
  4. \(x^2+y^2-3x+10y-15=0\) at (4, -11)
  5. \(x^2+y^2=40\) at the point whose abscissa is 2 and ordinate is -6

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Q.

  1. Find the equation of the tangent to the circle \(2x^2+2y^2=9\) which makes angle 45° with the x-axis.
  2. Find the equation of the normal to the circle \(2x^2+2y^2=9\) which makes angle 45° with the x-axis.

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Q.

  1. Show that the line 3x-4y=25 and the circle \(x^2+y^2 =25\) intersect in two coincident points.
  2. Prove that the line \(5x+12y+78=0\) is tangent to the circle \(x^2+y^2=36\).
  3. Prove that the tangent to the circle \(x^2+y^2=5 at the point (1, -2) also touches the circle \(x^2+y^2-8x+6y+20=0\) and find the point of contact.

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Q.

Find the equation of the tangents to the circle

  1. \(x^2+y^2=4\), which are parallel to \(3x+4y-5=0\),
  2. \(x^2+y^2=5\), which are perpendicular to \(x+2y=0\),
  3. \(x^2+y^2-6x+47=12\), which are parallel to the line \(4x+3y+5=0\),
  4. \(x^2+y^2-2x-4y-4=0\), which are perpendicular to the line \(3x-4y=1\).

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