MCA Entrance Previous Year Question Bank

If $3x+4y+k=0$ is tangent to the hyperbola $9x^2-16y^2=144$, then value of $k$ is:

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 the value of $b^2$ is:

If $e$ and $e^{\prime }$ be the eccentricities of a hyperbola and its conjugate, then $\frac{1}{e^2}+\frac{1}{e^{\prime 2}}$ is equal to:

The angle between the asymptotes of the hyperbola $27x^2-9y^2=24$ is:

If $PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that $△OPQ$ is an equilateral triangle, where $O$ is the centre of the hyperbola, then which of the following is true?

If the foci of the ellipse $b^2{x}^2+16y^2=16b^2$ and the hyperbola $81x^2-144y^2=\frac{81\times 144}{25}$ coincide, then the value of $b$, is:

The equation of the hyperbola with center at the origin, length of the transverse axis is 6 and one focus at (0, 4) is?

Find the foci of the equation $x^2+2x-4y^2+8y-7=0$.

Let $F_1,F_2$ be the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ (a>0, b>0), and let $O$ be the origin. Let $M$ be an arbitrary point on curve $C$ above the $X$-axis such that $M{F}_2\perp F_1{F}_2$. Let $H$ be a point on $M{F}_1$ such that $M{F}_1\perp OH$. If $|OH|=\lambda |O{F}_2|$ with $\lambda \in (\frac{2}{5},\frac{3}{5})$, then find the range of the eccentricity $e$.

Let $F_1,F_2$ be the foci of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ (a>0, b>0), and let $O$ be the origin. Let $M$ be an arbitrary point on curve $C$ above the $X$-axis and $H$ be a point on $M{F}_1$ such that $M{F}_2\perp F_1{F}_2$, $M{F}_1\perp OH$, and $|OH|=\lambda |O{F}_2|$ with $\lambda \in (2/5,3/5)$. Then the range of the eccentricity $e$ is: