Vinod Singh and Shweta Pawar Solutions for Chapter: Circle and Conics, Exercise 2: Critical Thinking

The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are

The equation of the directrices of the conic $x^2+2x-y^2+5=0$ are

The latus rectum of the hyperbola $9x^2-16y^2+72x-32y-16=0$ is

The locus of the point of intersection of the lines $ax\sec \theta +by\tan \theta =a$ and $ax\tan \theta + by\sec \theta =b$, where $\theta$ is the parameter, is

The equation $x=\frac{1}{2}\left(t+\frac{1}{t}\right), y=\frac{1}{2}\left(t-\frac{1}{t}\right)$, $t\ne 0$ represents

The locus of the point of intersection of the lines $bxt-ayt=ab$ and $bx+ay=abt$ is

If $e$ and ${\mathrm{e}}^{\text{'}}$are the eccentricities of the ellipse $5x^2+9y^2=45$ and the hyperbola $5x^2-4y^2=45$, then ${\mathrm{ee}}^{\text{'}}=$

The centres of the circles $x^2+y^2=1, x^2+y^2+6x-2y=1$ and $x^2+y^2-12x+4y=1$ are