Ellipse Q (1 Viewer)

learninstudent · Mar 22, 2010

ive forgotten how to do this... a little help to start off for these questins is muchly appreciated
1. p(acos theta, b sin theta) is any point on ellipse x^2/a^2 + y^2/b^2= 1
M is midpoint of SP where S is focus
find coord of M

2. for what vakues of k does equantion
x^2/ 29-k + y^2/ 4-k = 1
a) represent an elliipse
b) show that foci of elipse in a is independent of k

js992 · Mar 22, 2010

learninstudent said:
ive forgotten how to do this... a little help to start off for these questins is muchly appreciated
1. p(acos theta, b sin theta) is any point on ellipse x^2/a^2 + y^2/b^2= 1
M is midpoint of SP where S is focus
find coord of M

2. for what vakues of k does equantion
x^2/ 29-k + y^2/ 4-k = 1
a) represent an elliipse
b) show that foci of elipse in a is independent of k

1. Use your basic midpoint formula

M - (acos theta + ae) /2 , (bsin theta + 0 ) /2

2. The equation of an ellipse has the general form
$\frac{x^2}{a^2}+\frac{y^2}{b^2} = 1 (a,b>0)$
$\therefore \\29-k >0\\ 4-k > 0\\ 4>k$

For the next one, determine what your value of A and E is , and solve algebratically, knowing foci is (ae , 0 )

$$Foci = ae$\\ a^2 = 29-k\\ b^2 = 4-k\\ e^2 = 1-\frac{b^2}{a^2}\\ e^2 = 1-\frac{4-k}{29-k}\\ e = \sqrt{1-\frac{4-k}{29-k}}\\ a = \sqrt{29-k}\\ \therefore ae = \sqrt{(1-\frac{4-k}{29-k})(29-k)}\\ = \sqrt{29-k-(4-k)}\\ = \sqrt{25}\\ = 5$

Ellipse Q (1 Viewer)

learninstudent

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js992

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