Find the equation for the ellipse that satisfies the given conditions:

    Q19.    Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).

Answers (1)

Given,in an ellipse

Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).

Since, The major axis of this ellipse is on the Y-axis, the equation of the ellipse will be of the form:

 \frac{x^2}{b^2}+\frac{y^2}{a^2}=1

Where a and b are  the length of the semimajor axis and semiminor axis respectively.

Now since the ellipse passes through points,(3, 2) 

\frac{3^2}{b^2}+\frac{2^2}{a^2}=1

{9a^2+4b^2}={a^2b^2}

since the ellipse also  passes through points,(1, 6).

\frac{1^2}{b^2}+\frac{6^2}{a^2}=1

a^2+36b^2=a^2b^2

On solving these two equation we get

a^2=40 and b^2=10

Thus, The equation of the ellipse will be 

\frac{x^2}{10}+\frac{y^2}{40}=1.

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