# Recent questions and answers in Class11

### If the foci of the ellipse $\large\frac{x^2}{16}+\frac{y^6}{b^2}$$=1 and the hyperbola. \large\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25} coincide, then the value of b^2 is ### Angle between the asymptotes of the hyperbola 3x^2+7xy+2y^2-11x-7y+10=0 is ### If e_1 and e_2 are the eccentricities of the hyperbolas \large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$ and $\large\frac{y^2}{b^2}-\frac{x^2}{a^2}$$=1 Then value of \large\frac{1}{e_1^2}+\frac{1}{e_2^2} is ### The value of P for which the sum of squares of roots of equation x^2-(p-2)x-(p+1)=0 attains the least value is : ### The vertices of the hyperbola 9x^2-16y^2-36x+96y-252=0 are ### The diameter of 16x^2-9y^2=144 which is conjugate to x=2y is ### A common tangent to 9x^2-16y^2=144 and x^2+y^2=9 is ### The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is ### Find the asymptotes of the hyperbola. xy=4x+3y ### Find the equation of the hyperbola with focus (2,2) \; e=2 and directrise x+y=9 ### The minimum area of triangle formed by the tangents to the ellipse \large\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 coordinate axes is : ### The locus of the mid- points of the portion of the tangents to the ellipse intercepted between the axis is : ### Equation of the director circle of the ellipse x^2+2y^2+2x-12y+15=0 is ### If 3x+2y=0 and 5x-12y=0 are the equation of the pour of conjugates diameters, then value of eccentricity e is ### The locus of the mid -point of the portion of the tangents to the ellipse intercepted between the axes is ### Tangent is drawn to the ellipse \large\frac{x^2}{27}$$+y^2=1$ at $(3 \sqrt 3 \cos \theta, \sin \theta)$ (where $\theta \in (0, \large\frac{\pi}{2} )$) Then the value of $\theta$ such that sum of intercepts on axis made by this tangent is minimum is

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