2nd Year Math Chapter 6 Notes

Handwritten notes of 2nd Year Math Chapter 6 Notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of 2nd year math chapter 6 notes pdf for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.

• Important 2nd year math chapter 6 mcqs for Intermediate part-II students.
• 1. Focus of y^2=-4ax is 
• (a) (0,a) (b) (-a,0)            (c) (a,0) (d) (0,-a)
• 2. A type of the conic that has eccentricity greater than 1 is
• (a) An ellipse (b)  A parabola            (c) A hyperbola (d) A circle
• 3. x^2+y^2=-5 represents the 
• (a) Real circle (b) Imaginary circle (c)  Point circle      (d) None of these
• 4. Which one is related to circle 
• (a)  e=1 (b) e>1             (c) e<1 (d)  e=0 
• 5. Circle is the special case of :
• (a) Parabola (b)  Hyperbola (c)  Ellipse            (d)  None of these
• Important 2nd year math ch 6 mcqs for Intermediate part-II students.
• 6. Equation of the directrix of x^2=-4ay is:
• (a) x+a=0 (b)   x-a=0 (c)   y+a=0    (d)   y-a=0 
• 7. The midpoint of the foci of the ellipse is its
• (a) Vertex (b) Centre  (c) Directrix (d) None of these
• 8. Focus of the ellipse always lies on the
• (a) Minor axis (b) Major axi            (c) Directrix (d) None of these
• 9. Length of the major axis of x^2/a^2 +y^2/b^2 =1 ,a>b is
•  (a) 2a    (b)    2b (c)    (2b^2)/a (d) None of these
• Important 2nd year maths chapter 6 mcqs solved for Intermediate part-II students.
• 10. In the cases of ellipse it is always true that:
• (a) a^2>b^2  (b) a^2             (c)     a^2=b^2 (d)  a<0,b<0
• 11. Two conics always intersect each other in ______ points
• (a) No (b) one             (c) two (d)  four  
• 12. The eccentricity of ellipse x^2/16+y^2/9=1 is
• (a) √7/4                 (b)     7/4                          (c) 16            (d) 9
• 13. The foci of an ellipse are (4,1) and (0,1) then its centre is:
• (a) (4,2) (b) (2,1)                (c) (2,0) (d) (1,2)
• Important 2nd year maths chapter 6 mcqs for Intermediate part-II students.
• 14. The foci of hyperbola always lie on:
• (a)  x-axis (b)  Transverse axis (c) y-axis            (d) Conjugate axis 
• 15. Length of transverse axis of the hyperbola x^2/a^2 -y^2/b^2 =1 is
• (a) 2a             (b) 2b                          (c) a            (d) b
• 16. x^2/a^2 -y^2/b^2 =1  is symmetric about the:
•  (a)  y-axis (b)    x-axis         (c)  Both (a) and (b) (d)  None of these
• 17. Two vectors are said to be negative of each other if they have the same magnitude and ____direction.
• (a) Same (b)  opposite            (c) negative (d) parallel
• Important 2nd year maths chapter 6 mcqs with answers for Intermediate part-II students.
• 18. Parallelogram law of vector addition to describe the combined action of two forces, was used by
• (a) Cauchy (b)  Aristotle (c) Alkhwarzmi (d) Leibnitz 
• 19. The vector whose initial point is at the origin and terminal point is P , is called
• (a) Null vector (b) unit vector (c)  position vector (d) normal vector
• Important 2nd year math chapter 6 important questions for Intermediate part-II students.
• Write equations of tangent lines to the circle x^2+y^2+4x+2y=0 down from the point P(-1,2). Also find the tangential distance. 
• Prove that in any triangle ABC by vector method a^2=b^2+c^2-2bccos⁡A
• Find equation of ellipse having vertices (0,±5) and eccentricity 3/5.
• Important 2nd year math chapter 6 examples for Intermediate part-II students.
• Find an equation of the circle passing through the point (-2,-5) and touching the line 3x+4y-24=0 at the point (4,3)
• Find the foci, vertex and directrix of the parabola y=6x^2-1.,
• Find equations of the tangents to the circle x^2+y^2=2
• Find an equation of an ellipse with Foci (-3√3,0) and vertices (±6,0)
• Important 2nd year math exercise 6.1 solution pdf for Intermediate part-II students.
• Find equation of the circle passing through A(a,0),B(0,b) and C(0,0)
• Find an equation of the parabola with focus (1,2) and vertex (3,2),
• Important 2nd year math chapter 6 for Intermediate part-II students.
• Write an equation of the circle that passes through the point A(a,0),B(0,b),C (0,0),
• Write an equation of the circle that passes through the points A(4,5),B(-4,-3), and C(8,-3).
• Show that the equation 9x^2-18x+4y^2+8y-23=0 represent an ellipse. Find its elements (foci, vertices and directrices) 
• Show that the equation x^2+16x+4y^2-16y+76=0 represent an ellipse. Find its foci eccentricity, vertices and directrices. 
• Important 2nd year math chapter 6 exercise 6.1 for Intermediate part-II students.
• Important 2nd year math chapter 6 exercise 6.2 for Intermediate part-II students.
• Important 2nd year math chapter 6 exercise 6.3 for Intermediate part-II students.
• Important 2nd year math chapter 6 exercise 6.4 for Intermediate part-II students.
• Important 2nd year math chapter 6 exercise 6.5 for Intermediate part-II students.
• Important 2nd year math chapter 6 exercise 6.6 for Intermediate part-II students.