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Analytic Geometry
: What is the eccentricity of the ellipse shown below?
(x-5)^2 (y+1)^2
--------- + ----------- = 1
52 64
A: √3
B: 2/√3
C: √3/4
D: √3/2
(x-5)^2 (y+1)^2
--------- + ----------- = 1
52 64
A: √3
B: 2/√3
C: √3/4
D: √3/2
Analytic Geometry
: How long is the minor axis for the ellipse shown below?
(x+4)^2 (y-1)^2
---------- + ---------- = 1
25 16
A: 8
B: 9
C: 12
D: 18
: Which of the following correctly represents the coordinates of the foci of the ellipse shown below?
(x-7)^2 (y+3)^2
--------- + ------------ = 1
4 16
A: (7, - 3 ± 2 √5)
B: (7 ± 2 √5, -3)
C: (7, - 3 ± 2 √3)
D: (7 ± 2 √3, - 3)
(x+4)^2 (y-1)^2
---------- + ---------- = 1
25 16
A: 8
B: 9
C: 12
D: 18
: Which of the following correctly represents the coordinates of the foci of the ellipse shown below?
(x-7)^2 (y+3)^2
--------- + ------------ = 1
4 16
A: (7, - 3 ± 2 √5)
B: (7 ± 2 √5, -3)
C: (7, - 3 ± 2 √3)
D: (7 ± 2 √3, - 3)
Analytic Geometry
: What are the coordinates of the center of the ellipse shown below?
(x-1)^2 (y+5)^2
--------- + ----------- = 1
9 16
A: (5, -1)
B: (1, -5)
C: (3,4)
D: (-3, -4)
: What is the length of the major axis of the ellipse shown below?
(x-1)^2 (y+5)^2
--------- + ---------- = 1
9 16
A: 4
B: 8
C: 32
D: 16
(x-1)^2 (y+5)^2
--------- + ----------- = 1
9 16
A: (5, -1)
B: (1, -5)
C: (3,4)
D: (-3, -4)
: What is the length of the major axis of the ellipse shown below?
(x-1)^2 (y+5)^2
--------- + ---------- = 1
9 16
A: 4
B: 8
C: 32
D: 16
Analytic Geometry
Q. Draw the graph of following functions on graph paper.
(i)y=x2
(ii)y=x2+1
(iii)y2=x
(iv)y2=4x+2
(v)y2=x-1
(vi)x2=4y
(vii)x2=4y-1
(viii)x2+y2=1
(ix)x2-y2=1
(xx)x2+y2=0
(i)y=x2
(ii)y=x2+1
(iii)y2=x
(iv)y2=4x+2
(v)y2=x-1
(vi)x2=4y
(vii)x2=4y-1
(viii)x2+y2=1
(ix)x2-y2=1
(xx)x2+y2=0
Analytic Geometry
Identify the center and radius of the circle (x + 2)^2 + (y – 3)^2 = 9
Check all that apply
Center: (2, -3) r = 3
Center: (2, -3) r = 9
Center: (-2, 3) r = 3
Center: (-3, 2) r = 9
What is the radius of a circle with the equation x^2 + y^2 + 2x + 4y – 9 = 0
Round your answer to the nearest thousandth. _____________
Which of the following is a degenerate circle?
Check all that apply
x + y = 7
x^2 + y^2 = -2
x^2 + y^2 = 5
(x – 5)^2 + (y – 3)^2 = 0
Check all that apply
Center: (2, -3) r = 3
Center: (2, -3) r = 9
Center: (-2, 3) r = 3
Center: (-3, 2) r = 9
What is the radius of a circle with the equation x^2 + y^2 + 2x + 4y – 9 = 0
Round your answer to the nearest thousandth. _____________
Which of the following is a degenerate circle?
Check all that apply
x + y = 7
x^2 + y^2 = -2
x^2 + y^2 = 5
(x – 5)^2 + (y – 3)^2 = 0
Analytic Geometry
Show that the line through the centre perpendicular to the normal at any point does not
meet the hyperbola.
meet the hyperbola.
Analytic Geometry
Find the equations of the chords of the parabola y2 = 4ax which pass through the point (–6a, 0) and which subtends an angle of 45° at the vertex.
Analytic Geometry
Let S is the focus of the parabola y2 = 4ax and X the foot of the directrix, PP' is a double ordinate of the curve and PX meets the curve again in Q. Prove that P'Q passes through focus.
Analytic Geometry
Find the equations of the tangents of the parabola y2 = 12x, which passes through the point (2,5).
Analytic Geometry
If lines be drawn parallel to the axes of co-ordinates from the points where x cosα + y sinα = p meets them so as to meet the perpendicular on this line from the origin in the points P and Q then prove that | PQ | = 4p | cos2α | cosec^2(2α.)
