Question
Download Solution PDFThe equations of the ellipse whose vertices are (±10, 0) and foci at (±9, 0) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFSince vertices of an ellipse are (±a, 0) and foci are (±ae, 0)
∴ a = 10 and ae = 9
\(e = \frac{9}{{10}}\)
Where e is the eccentricity of ellipse,
We know, \({e^2} = 1 - \frac{{{b^2}}}{{{a^2}}}\)
\(\begin{array}{l} \Rightarrow \frac{{81}}{{100}} = 1 - \frac{{{b^2}}}{{100}}\\ \frac{{{b^2}}}{{100}} = \frac{19}{{100}} \Rightarrow {b^2} = 19 \end{array}\)
Hence, required equation of ellipse is
\(\begin{array}{l} \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\\ \frac{{{x^2}}}{{100}} + \frac{{{y^2}}}{19} = 1 \end{array}\)
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