120575
If \(\alpha, \beta\) are the eccentric angles of the extremities of a focal chord (other than the major axis) of the ellipse \(x^2+4 y^2-4\) then \(\sqrt{3} \cos \frac{\alpha+\beta}{2}=\)
120576
In the ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentricity is
1 \(\frac{1}{2}\)
2 \(\frac{7}{5}\)
3 \(\frac{1}{\sqrt{5}}\)
4 \(\frac{3}{5}\)
Explanation:
D Given, \(2 \mathrm{ae}=6\)
And, minor axis
\(2 \mathrm{~b}=8\)
We known that,
\(b^2=a^2\left(1-e^2\right)\)
\((4)^2=a^2-a^2 e^2\)
\((4)^2=a^2-(3)^2\)
\(a^2=25\)
\(a=5\)
\(2 a e=6\)
\(e=\frac{3}{5}\)
and
\(\therefore \quad \mathrm{e}=\frac{3}{5}\)
120575
If \(\alpha, \beta\) are the eccentric angles of the extremities of a focal chord (other than the major axis) of the ellipse \(x^2+4 y^2-4\) then \(\sqrt{3} \cos \frac{\alpha+\beta}{2}=\)
120576
In the ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentricity is
1 \(\frac{1}{2}\)
2 \(\frac{7}{5}\)
3 \(\frac{1}{\sqrt{5}}\)
4 \(\frac{3}{5}\)
Explanation:
D Given, \(2 \mathrm{ae}=6\)
And, minor axis
\(2 \mathrm{~b}=8\)
We known that,
\(b^2=a^2\left(1-e^2\right)\)
\((4)^2=a^2-a^2 e^2\)
\((4)^2=a^2-(3)^2\)
\(a^2=25\)
\(a=5\)
\(2 a e=6\)
\(e=\frac{3}{5}\)
and
\(\therefore \quad \mathrm{e}=\frac{3}{5}\)
120575
If \(\alpha, \beta\) are the eccentric angles of the extremities of a focal chord (other than the major axis) of the ellipse \(x^2+4 y^2-4\) then \(\sqrt{3} \cos \frac{\alpha+\beta}{2}=\)
120576
In the ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentricity is
1 \(\frac{1}{2}\)
2 \(\frac{7}{5}\)
3 \(\frac{1}{\sqrt{5}}\)
4 \(\frac{3}{5}\)
Explanation:
D Given, \(2 \mathrm{ae}=6\)
And, minor axis
\(2 \mathrm{~b}=8\)
We known that,
\(b^2=a^2\left(1-e^2\right)\)
\((4)^2=a^2-a^2 e^2\)
\((4)^2=a^2-(3)^2\)
\(a^2=25\)
\(a=5\)
\(2 a e=6\)
\(e=\frac{3}{5}\)
and
\(\therefore \quad \mathrm{e}=\frac{3}{5}\)
120575
If \(\alpha, \beta\) are the eccentric angles of the extremities of a focal chord (other than the major axis) of the ellipse \(x^2+4 y^2-4\) then \(\sqrt{3} \cos \frac{\alpha+\beta}{2}=\)
120576
In the ellipse, if the distance between the foci is 6 units and the length of its minor axis is 8 units, then its eccentricity is
1 \(\frac{1}{2}\)
2 \(\frac{7}{5}\)
3 \(\frac{1}{\sqrt{5}}\)
4 \(\frac{3}{5}\)
Explanation:
D Given, \(2 \mathrm{ae}=6\)
And, minor axis
\(2 \mathrm{~b}=8\)
We known that,
\(b^2=a^2\left(1-e^2\right)\)
\((4)^2=a^2-a^2 e^2\)
\((4)^2=a^2-(3)^2\)
\(a^2=25\)
\(a=5\)
\(2 a e=6\)
\(e=\frac{3}{5}\)
and
\(\therefore \quad \mathrm{e}=\frac{3}{5}\)