Analytic Geometry Answers

: 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

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

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

Show that the line through the centre perpendicular to the normal at any point does not
meet the hyperbola.

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.

Find the equations of the tangents of the parabola y2 = 12x, which passes through the point (2,5).

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.)

Find the co-ordinates of the orthocentre of the triangle, the equations of whose sides are x + y = 1,2x + 3y = 6, 4x − y + 4 = 0, without finding the co−ordinates of its vertices.

Trisect the segment connecting P(-5,2) and Q(3,-4).

Find y so that the length of the segment joining P(-2, 1) and Q(3, y) is square root of 34.