Standard Equation of Ellipse
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Ellipse

120508 The eccentricity of the ellipse whose major axis is three times the minor axis is:

1 \(\frac{\sqrt{2}}{3}\)
2 \(\frac{\sqrt{3}}{2}\)
3 \(\frac{2 \sqrt{2}}{3}\)
4 \(\frac{2}{\sqrt{3}}\)
VITEEE-2018
Ellipse

120509 The foci of the ellipse \(\frac{x^2}{16}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}\) coincide then value of \(b^2\) is

1 1
2 5
3 7
4 9
VITEEE-2016
Ellipse

120510 The minimum area of the triangle formed by any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the coordinate axes is

1 \(a^2+b^2\)
2 \(\frac{(a+b)^2}{2}\)
3 ab
4 \(\frac{(a-b)^2}{2}\)
VITEEE-2014
Ellipse

120511 If the equation of an ellipse is \(3 x^2+2 y^2+6 x-8 y+5=0\), then which of the following are true?

1 \(e=\frac{1}{\sqrt{3}}\)
2 center is \((-1,2)\)
3 foci are \((-1,1)\) and \((-1,3)\)
4 All of the above
VITEEE-2010
Ellipse

120512 The equation of an ellipse with focus at \((1,-1)\), directrix \(x-y-3=0\) and eccentricity \(1 / 2\) is

1 \(7 x^2+2 x y+7 y^2+7=0\)
2 \(7 x^2+2 x y+7 y^2-10 x+10 y+7=0\)
3 \(7\left(x^2+y^2\right)+2 x y+10 x-10 y-7=0\)
4 \(7\left(x^2+y^2\right)+2 x y-10 x-10 y+7=0\)
UPSEE-2018
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Ellipse

120508 The eccentricity of the ellipse whose major axis is three times the minor axis is:

1 \(\frac{\sqrt{2}}{3}\)
2 \(\frac{\sqrt{3}}{2}\)
3 \(\frac{2 \sqrt{2}}{3}\)
4 \(\frac{2}{\sqrt{3}}\)
VITEEE-2018
Ellipse

120509 The foci of the ellipse \(\frac{x^2}{16}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}\) coincide then value of \(b^2\) is

1 1
2 5
3 7
4 9
VITEEE-2016
Ellipse

120510 The minimum area of the triangle formed by any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the coordinate axes is

1 \(a^2+b^2\)
2 \(\frac{(a+b)^2}{2}\)
3 ab
4 \(\frac{(a-b)^2}{2}\)
VITEEE-2014
Ellipse

120511 If the equation of an ellipse is \(3 x^2+2 y^2+6 x-8 y+5=0\), then which of the following are true?

1 \(e=\frac{1}{\sqrt{3}}\)
2 center is \((-1,2)\)
3 foci are \((-1,1)\) and \((-1,3)\)
4 All of the above
VITEEE-2010
Ellipse

120512 The equation of an ellipse with focus at \((1,-1)\), directrix \(x-y-3=0\) and eccentricity \(1 / 2\) is

1 \(7 x^2+2 x y+7 y^2+7=0\)
2 \(7 x^2+2 x y+7 y^2-10 x+10 y+7=0\)
3 \(7\left(x^2+y^2\right)+2 x y+10 x-10 y-7=0\)
4 \(7\left(x^2+y^2\right)+2 x y-10 x-10 y+7=0\)
UPSEE-2018
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NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Ellipse

120508 The eccentricity of the ellipse whose major axis is three times the minor axis is:

1 \(\frac{\sqrt{2}}{3}\)
2 \(\frac{\sqrt{3}}{2}\)
3 \(\frac{2 \sqrt{2}}{3}\)
4 \(\frac{2}{\sqrt{3}}\)
VITEEE-2018
Ellipse

120509 The foci of the ellipse \(\frac{x^2}{16}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}\) coincide then value of \(b^2\) is

1 1
2 5
3 7
4 9
VITEEE-2016
Ellipse

120510 The minimum area of the triangle formed by any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the coordinate axes is

1 \(a^2+b^2\)
2 \(\frac{(a+b)^2}{2}\)
3 ab
4 \(\frac{(a-b)^2}{2}\)
VITEEE-2014
Ellipse

120511 If the equation of an ellipse is \(3 x^2+2 y^2+6 x-8 y+5=0\), then which of the following are true?

1 \(e=\frac{1}{\sqrt{3}}\)
2 center is \((-1,2)\)
3 foci are \((-1,1)\) and \((-1,3)\)
4 All of the above
VITEEE-2010
Ellipse

120512 The equation of an ellipse with focus at \((1,-1)\), directrix \(x-y-3=0\) and eccentricity \(1 / 2\) is

1 \(7 x^2+2 x y+7 y^2+7=0\)
2 \(7 x^2+2 x y+7 y^2-10 x+10 y+7=0\)
3 \(7\left(x^2+y^2\right)+2 x y+10 x-10 y-7=0\)
4 \(7\left(x^2+y^2\right)+2 x y-10 x-10 y+7=0\)
UPSEE-2018
NEET DIGITAL LIBRARY
Ellipse

120508 The eccentricity of the ellipse whose major axis is three times the minor axis is:

1 \(\frac{\sqrt{2}}{3}\)
2 \(\frac{\sqrt{3}}{2}\)
3 \(\frac{2 \sqrt{2}}{3}\)
4 \(\frac{2}{\sqrt{3}}\)
VITEEE-2018
Ellipse

120509 The foci of the ellipse \(\frac{x^2}{16}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}\) coincide then value of \(b^2\) is

1 1
2 5
3 7
4 9
VITEEE-2016
Ellipse

120510 The minimum area of the triangle formed by any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the coordinate axes is

1 \(a^2+b^2\)
2 \(\frac{(a+b)^2}{2}\)
3 ab
4 \(\frac{(a-b)^2}{2}\)
VITEEE-2014
Ellipse

120511 If the equation of an ellipse is \(3 x^2+2 y^2+6 x-8 y+5=0\), then which of the following are true?

1 \(e=\frac{1}{\sqrt{3}}\)
2 center is \((-1,2)\)
3 foci are \((-1,1)\) and \((-1,3)\)
4 All of the above
VITEEE-2010
Ellipse

120512 The equation of an ellipse with focus at \((1,-1)\), directrix \(x-y-3=0\) and eccentricity \(1 / 2\) is

1 \(7 x^2+2 x y+7 y^2+7=0\)
2 \(7 x^2+2 x y+7 y^2-10 x+10 y+7=0\)
3 \(7\left(x^2+y^2\right)+2 x y+10 x-10 y-7=0\)
4 \(7\left(x^2+y^2\right)+2 x y-10 x-10 y+7=0\)
UPSEE-2018
Join With Us for More Updates
Ellipse

120508 The eccentricity of the ellipse whose major axis is three times the minor axis is:

1 \(\frac{\sqrt{2}}{3}\)
2 \(\frac{\sqrt{3}}{2}\)
3 \(\frac{2 \sqrt{2}}{3}\)
4 \(\frac{2}{\sqrt{3}}\)
VITEEE-2018
Ellipse

120509 The foci of the ellipse \(\frac{x^2}{16}+\frac{y^2}{b^2}=1\) and the hyperbola \(\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}\) coincide then value of \(b^2\) is

1 1
2 5
3 7
4 9
VITEEE-2016
Ellipse

120510 The minimum area of the triangle formed by any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the coordinate axes is

1 \(a^2+b^2\)
2 \(\frac{(a+b)^2}{2}\)
3 ab
4 \(\frac{(a-b)^2}{2}\)
VITEEE-2014
Ellipse

120511 If the equation of an ellipse is \(3 x^2+2 y^2+6 x-8 y+5=0\), then which of the following are true?

1 \(e=\frac{1}{\sqrt{3}}\)
2 center is \((-1,2)\)
3 foci are \((-1,1)\) and \((-1,3)\)
4 All of the above
VITEEE-2010
Ellipse

120512 The equation of an ellipse with focus at \((1,-1)\), directrix \(x-y-3=0\) and eccentricity \(1 / 2\) is

1 \(7 x^2+2 x y+7 y^2+7=0\)
2 \(7 x^2+2 x y+7 y^2-10 x+10 y+7=0\)
3 \(7\left(x^2+y^2\right)+2 x y+10 x-10 y-7=0\)
4 \(7\left(x^2+y^2\right)+2 x y-10 x-10 y+7=0\)
UPSEE-2018