Get the Power
Chapter 11
CONIC SECTION
CIRCLE:
The equation of a circle with centre at (h, k) and radius r is ( ( ) Equation of a circle with centre at origin and radius r is PARABOLA( Symmetric about its axis) Right Equation Axis Figure y=0 Left y= 0 Upward x= 0
)
Downward x= 0
Focus (a, 0) (-a, 0) Vertex (0,0) (0,0) Latus 4a 4a Rectum Directrix x = -a x=a ELLIPSE ( Symmetric about both the axis) Equation Equation of the major axis Length of major axis Length of minor axis Vertices Foci Eccentricity Latus Rectum y=0 2a 2b ( a, 0) ( c, 0)
(0, a) (0,0) 4a y = -a
(0, -a) (0,0) 4a y =a
x=0 2a 2b (0, a ) (0, c )
HYPERBOLA Equation Equation of the transverse axis Length of transverse axis Length of conugate axis Vertices Foci Eccentricity Latus Rectum y =0 2a 2b ( a, 0) ( c, 0) x =0 2a 2b (0, a ) (0, c )
TEXT BOOK QUESTIONS * →Exercise 11.1 * → Exercise 11.2 * → Exercise 11.3 * →Exercise 11.4 * →Example ** →Exercise 11.1 ** → Exercise 11.2 ** → Exercise 11.3 ** → Exercise 11.4 Extra Questions: 1.Find the centre and the radius of 3x2 + 3y2 + 6x -4y -1 =0 (ans : (-1, 2/3), 4/3) 2. Find the value of p so that x2 + y2 + 8x +10y +p =0, is the equation of the circle of radius 7 units. (ans : -8) 3. Find the equation of the circle when the end points of the diameter are A ( -2 ,3), B ( 3, -5) ( ans: x2 + y2 -x +2y -21 =0 ) Qns 10,11 Qns 5,6,8 Qns 5,6,7,8,9,10 Qns 4,5,6 → 4,17,18,19 Qns 9,12,13,14 Qns 11,12 Qns 13 to Qns 20 Qns 10 to Qns 15
4. Find the equation of the circle circumscribing the triangle formed by the straight lines: x + y = 6, 2x + y =4 and x +2y = 5 (ans: x2 + y2 -17x -19y +50 =0 ) 5. Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum. ( ans : ½ x 12 x 3 sq.units) 6. Find the equation of the ellipse with eccentricity ¾ , foci on y- axis , center at the origin and passes through the point ( 6, 4) ( ans: 16x2 + 7y2 = 688) 7. Find the length of major axis and minor axis of 4x2 +y2 =
CONIC SECTION
CIRCLE:
The equation of a circle with centre at (h, k) and radius r is ( ( ) Equation of a circle with centre at origin and radius r is PARABOLA( Symmetric about its axis) Right Equation Axis Figure y=0 Left y= 0 Upward x= 0
)
Downward x= 0
Focus (a, 0) (-a, 0) Vertex (0,0) (0,0) Latus 4a 4a Rectum Directrix x = -a x=a ELLIPSE ( Symmetric about both the axis) Equation Equation of the major axis Length of major axis Length of minor axis Vertices Foci Eccentricity Latus Rectum y=0 2a 2b ( a, 0) ( c, 0)
(0, a) (0,0) 4a y = -a
(0, -a) (0,0) 4a y =a
x=0 2a 2b (0, a ) (0, c )
HYPERBOLA Equation Equation of the transverse axis Length of transverse axis Length of conugate axis Vertices Foci Eccentricity Latus Rectum y =0 2a 2b ( a, 0) ( c, 0) x =0 2a 2b (0, a ) (0, c )
TEXT BOOK QUESTIONS * →Exercise 11.1 * → Exercise 11.2 * → Exercise 11.3 * →Exercise 11.4 * →Example ** →Exercise 11.1 ** → Exercise 11.2 ** → Exercise 11.3 ** → Exercise 11.4 Extra Questions: 1.Find the centre and the radius of 3x2 + 3y2 + 6x -4y -1 =0 (ans : (-1, 2/3), 4/3) 2. Find the value of p so that x2 + y2 + 8x +10y +p =0, is the equation of the circle of radius 7 units. (ans : -8) 3. Find the equation of the circle when the end points of the diameter are A ( -2 ,3), B ( 3, -5) ( ans: x2 + y2 -x +2y -21 =0 ) Qns 10,11 Qns 5,6,8 Qns 5,6,7,8,9,10 Qns 4,5,6 → 4,17,18,19 Qns 9,12,13,14 Qns 11,12 Qns 13 to Qns 20 Qns 10 to Qns 15
4. Find the equation of the circle circumscribing the triangle formed by the straight lines: x + y = 6, 2x + y =4 and x +2y = 5 (ans: x2 + y2 -17x -19y +50 =0 ) 5. Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum. ( ans : ½ x 12 x 3 sq.units) 6. Find the equation of the ellipse with eccentricity ¾ , foci on y- axis , center at the origin and passes through the point ( 6, 4) ( ans: 16x2 + 7y2 = 688) 7. Find the length of major axis and minor axis of 4x2 +y2 =