Find the equation of ellipse whose centre is C(4,3) and focus S(2,3) eccentricity e=1/2[.5] Is this a case of tilted ellipse ? Plz explain the solution

Hello Vinay


As u see the C and S has common y-co-ordinate..it means both C and S lies on same line y=3
So y=3 is the major axis...


Distance between CS = ae (distance between two focus is 2ae)

CS = 2

So ae = 2

a = 4

Now  e^2 = 1 - (b/a)^2   => 1/4 = 1 - ( b/4)^2

=> (b/4)^2 = 3/4

b/4 = root(3)/2

b= 2.root(3)

Equation when center is (h,k) with and major axis with a ( a>b) and minor with b..

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

and if b>a  then  (x-h)^2/a^2 + (y-k)^2/b^2 = 1

=> (x-4)^2/4 + (y-3)^2/12 = 1   ans,

With regards

Yagya

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