120534 Let a line \(L\) pass through the point of intersection of the lines \(b x+10 y-8=0\) and \(2 x\) \(-3 y=0, b \in R-\left\{\frac{4}{3}\right\}\). If the line \(L\) also passes through the point \((1,1)\) and touches the circle \(17\left(x^2+y^2\right)=16\) then the eccentricity of the ellipse \(\frac{x^2}{5}+\frac{y^2}{b^2}=1\) is :

120535 Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4}=1, a>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6 \sqrt{3}\). Then the eccentricity of the ellipse is:

120536 Let the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>\) b, be \(\frac{1}{4}\). If this ellipse passes through the point \(\left(-4 \sqrt{\frac{2}{5}}, 3\right)\), then \(a^2+b^2\) is equal to :

120537 If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b\lt 2\), from the origin is 1 , then the eccentricity of the ellipse is :

120534 Let a line \(L\) pass through the point of intersection of the lines \(b x+10 y-8=0\) and \(2 x\) \(-3 y=0, b \in R-\left\{\frac{4}{3}\right\}\). If the line \(L\) also passes through the point \((1,1)\) and touches the circle \(17\left(x^2+y^2\right)=16\) then the eccentricity of the ellipse \(\frac{x^2}{5}+\frac{y^2}{b^2}=1\) is :

120535 Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4}=1, a>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6 \sqrt{3}\). Then the eccentricity of the ellipse is:

120536 Let the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>\) b, be \(\frac{1}{4}\). If this ellipse passes through the point \(\left(-4 \sqrt{\frac{2}{5}}, 3\right)\), then \(a^2+b^2\) is equal to :

120537 If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b\lt 2\), from the origin is 1 , then the eccentricity of the ellipse is :

120534 Let a line \(L\) pass through the point of intersection of the lines \(b x+10 y-8=0\) and \(2 x\) \(-3 y=0, b \in R-\left\{\frac{4}{3}\right\}\). If the line \(L\) also passes through the point \((1,1)\) and touches the circle \(17\left(x^2+y^2\right)=16\) then the eccentricity of the ellipse \(\frac{x^2}{5}+\frac{y^2}{b^2}=1\) is :

120535 Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4}=1, a>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6 \sqrt{3}\). Then the eccentricity of the ellipse is:

120536 Let the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>\) b, be \(\frac{1}{4}\). If this ellipse passes through the point \(\left(-4 \sqrt{\frac{2}{5}}, 3\right)\), then \(a^2+b^2\) is equal to :

120537 If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b\lt 2\), from the origin is 1 , then the eccentricity of the ellipse is :

120534 Let a line \(L\) pass through the point of intersection of the lines \(b x+10 y-8=0\) and \(2 x\) \(-3 y=0, b \in R-\left\{\frac{4}{3}\right\}\). If the line \(L\) also passes through the point \((1,1)\) and touches the circle \(17\left(x^2+y^2\right)=16\) then the eccentricity of the ellipse \(\frac{x^2}{5}+\frac{y^2}{b^2}=1\) is :

120535 Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4}=1, a>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6 \sqrt{3}\). Then the eccentricity of the ellipse is:

120536 Let the eccentricity of an ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>\) b, be \(\frac{1}{4}\). If this ellipse passes through the point \(\left(-4 \sqrt{\frac{2}{5}}, 3\right)\), then \(a^2+b^2\) is equal to :

120537 If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b\lt 2\), from the origin is 1 , then the eccentricity of the ellipse is :