Conic Sections ...

If the curves $$f(x) = e^{x}$$ and $$g(x) = kx^{2}$$ touches each other then the value of $$k$$ is equal to

Find the equation of the circle which passes through the point $$(1, 1)$$ & which touches the $$x^2 + y^2 + 4x - 6y - 3 = 0$$ at the point $$(2, 3)$$ on it.

Let circles $${C}_{1}$$ and $${C}_{2}$$ an Argand plane be given by $$\left| z+1 \right| =3$$ and $$\left| z-2 \right| =7\ \ $$ respectively. If a variable circle $$\left| z-{ z }_{ 0 } \right| =r\quad $$ be inside circle $${C}_{2}$$ such that it touches $${C}_{1}$$ externally and $${C}_{2}$$ internally then locus of $${z}_{0}$$ describes a conic $$E$$ whose eccentricity is equal to

Find the locus of the point of intersection of the lines $$\sqrt{3}x-y-4\sqrt{3} \lambda=0$$ and $$\sqrt{3}\lambda x+\lambda y-4\sqrt{3}=0$$ for different values of $$\lambda$$.

Find the equation of the circle which passes through the point (1, 1) & which touches the circle $$x^{2} + y^{2} + 4x - 6y - 3 = 0$$ at the point $$(2, 3)$$ on it.

The equation of the hyperbola whose foci are $$(6, 5), (-4, 5)$$ and eccentricity $$5/4$$ is?

If the curve y = | x- 3| touches the parabola $$y^2 = \lambda (x-4), \lambda >0$$, then latus rectum of the parabola, is

The equation of the circle passing through $$(4,\ 5)$$ having the centre at $$(2 ,\ 2)$$ is

If $$16{m}^{2}-8l-1=0,$$ then equation of the circle having $$lx+my+1=0$$ is a tangent is