Conic Sections ...

The equation of the circle having normal at $$(3, 3)$$ as $$y = x$$ and passing through $$(2, 2)$$ is:

The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola $$\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$$ is equal to (where $$e$$ is the eccentricity of the hyperbola)

If the equation $$\dfrac { \lambda { \left( x+1 \right)  }^{ 2 } }{ 3 } +\dfrac { { \left( y+2 \right)  }^{ 2 } }{ 4 }=1$$ represents a circle then $$\lambda=$$

If the equation $$\dfrac{\lambda (x+1)^2}{3}+\dfrac{(y+2)^2}{4}=1$$ represents a circle then $$\lambda = ?$$

The equation of the circle touches y axis and having radius $$2$$ units and centre is $$(-2, -3)$$?

The foci of the ellipse $$\dfrac{x^{2}}{16} + \dfrac{y^{2}}{b^{2}} =1$$ and the hyperbola $$\dfrac{x^{2}}{144} - \dfrac{y^{2}}{81} =\dfrac{1}{25}$$ coincide, then the value of $$b^{2}$$ is:

The radius of the circle $$x^2+y^2-5x+2y+5=0$$ is

Cantres of the three circles
$$x^{2}+y^{2}-4x-6y-14=0$$
$$x^{2}+y^{2}+2x+4y-5=0$$
and $$x^{2}+y^{2}-10x-16y+7=0$$

Coordinates of centre and radius of the circle $$(x-3)^2+(y+4)^2=25$$ are respectively

The parabola $$y = px^{2} + px + q$$ is symmetrical about the line