Vertices of an ellipse are (1,5) and (1,-5) and (3,0) is a point on the ellipse , What is the ellipse equation ?

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Answer 1 · 2018-05-18T08:55:16

Equation of ellipse is #(x-1)^2/4+y^2/25=1#

As vertices of ellipse are #(1,5)# and #(1-5)#, the center of ellipse is their midpoint i.e. #((1+1)/2,(5-5)/2)# or #(1,0)#

Further as distance between #(1,5)# and #(1-5)# is #10# and as they lie vertically one above the other, axis parallel to #y#-axis is #10#

and hence likely equation of ellipse is

#(x-1)^2/a^2+y^2/5^2=1#

Now, as it passes through #(3,0)#, we have

#(3-1)^2/a^2+0/5^2=1#

or #4/a^2=1# i.e. #a^2=4# and

equation of ellipse is #(x-1)^2/4+y^2/25=1#

graph{((x-1)^2/4+y^2/25-1)((x-1)^2+(y-5)^2-0.03)((x-1)^2+(y+5)^2-0.03)((x-3)^2+y^2-0.03)=0 [-12, 12, -6, 6]}