What is the equation of the ellipse centred at (2,1) passing through (1,0) and (2,-5)?

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Answer 1 · 2018-05-16T11:55:16

# x^2/(36/35)+y^2/36=1, or, 35x^2+y^2=36#.

We know that, the eqn. of an ellipse having centre at the

point #C=C(h,k)# is given by, # S : (x-h)^2/a^2+(y-k)^2/b^2=1#.

Since, in our case, #C=C(h,k)=C(2,1)#, we have,

# S : (x-2)^2/a^2+(y-1)^2/b^2=1#.

Given that, #(1,0) in S. :. (1-2)^2/a^2+(0-1)^2/b^2=1#.

#:. 1/a^2+1/b^2=1.............(1)#.

Similarly, #(2,-5) in S rArr (2-2)^2/a^2+(-5-1)^2/b^2=1#.

#:. 36/b^2=1 rArr 1/b^2=1/36#.

Then, by #(1), 1/a^2=1-1/b^2=1-1/36=35/36#.

Therefore, # S : x^2(35/36)+y^2(1/36)=1, or, 35x^2+y^2=36#.