Answers all the questions

Question

Question 1:

Suppose that an ellipse is centered at (0,0) and has a vertex (5,0) and focus (1,0). Find b=______. (round to 2 decimal places)

Question 2:

Suppose that an ellipse is centered at (0,0) and has a co-vertex (7,0) and focus (0,3). Find a=______. (round to 2 decimal places)



Question 6:

Given the standard equation of the ellipse shown below. 

(x-h)2b2+(y-k)2a2=1. What is b=____?

Answer 1

vertex (5,0), focus (1,0) center (0,0)

the ellipse is of the form x^2/a^2 +y^2/b^2 = 1

it's a vertical ellipse as the focus is on the y axis

to get (5,0) on the ellipse, y = 0 when x=5

5^2/5^2 + 0^2/b^2 = 1

x^2/25 + y^2/b^2 = 1

c = distance from center to a focus = 1

c^2 = a^2 -b^2

b^2 = a^2 -c^2 = 25-1 = 24

x^2/25 + y^2/24 = 1 is the ellipse's equation

b= sqr24 = 2sqr6 = about 4.899

= about 4.90

vertex (7,0) focus (0,3) center (0,0)

c=3, it's another vertical ellipse with major axis as the y axis

14 = the minor axis, vertical vertices are greater and less than 7 or -7

as the major axis > minor axis

a^2 = 49, c^2 =9

b^2 = 49-9 =40

b = sqr40 = 2sqr10 = about 6.32

a = 7

the problem may be switching a and b,

so go with 6.32 or 7 depending on how they're using the letters

(x-h)^2/b^2 + (y-h)^2/a^2 = 1

they seem to be using a for half the major axis

and b as half the minor (smaller) axis

b = half the minor axis

or the y coordinate of the vertex (b,h)

not easy to keep this straight.

no guarantees the above is error free

but refer to graphs and standard equations for ellipses

along with the equations for c^2, b^2 and a^2