D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Conic Sections, Exercise 2: Exercise 2

If the angle between the straight lines joining the foci to an extremity of minor axis in an ellipse be $90°$, then the eccentricity of the ellipse is

Which of the following options is not the asymptote of the curve $3x^3+2x^{2}y-7x{y}^2+2y^3-14xy+7y^2+4x+5y=0$?

If the tangent at the point $\left(4\cos \theta ,\frac{16}{\sqrt{11}}\sin \theta \right)$ to the ellipse $16x^2+11y^2=256$ is also a tangent to the circle $x^2+y^2-2x=15$, then the value of $\theta$ is

Find the equation of the ellipse having its centre at the point $C\left(2,-3\right)$, one focus at $S\left(3,-3\right)$ and one vertex at $A\left(4,-3\right)$.

The equation of tangents to the hyperbola $3x^2-2y^2=6$, which is perpendicular to the line $x-3y=3$, are

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $P\left(x_1,y_1\right), Q\left(x_2,y_2\right), R\left(x_3,y_3\right), S\left(x_4,y_4\right)$, then

The product of the perpendiculars drawn from the foci upon any tangent to an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, is equal to

The equation of one of the common tangents to the parabola $y^2=8x$ and $x^2+y^2-12x+4=0$ is