Conic Sections ...

If the tangent to the curve, $$y=x^3+ax-b$$ at the point $$(1, -5)$$ is perpendicular to the line, $$-x+y+4=0$$, then which one of the following points lies on the curve?

If the lines $$2\mathrm{x}+3\mathrm{y}+1=0$$ and $$\mathrm{3x}- \mathrm{y}-4=0$$ lie along diameters of a circle of circumference $$ 10\pi$$, then the equation of the circle is: 

If $$5x+9=0$$ is the directrix of the hyperbola $$16{x}^{2}-9{y}^{2}=144$$, then its correponding focus is:

If $${a}\neq 0$$ and the line  $$2{b}{x}+3 cy+4{d}=0$$ passes through the points of intersection of the parabolas $${y}^{2}=4ax$$ and $${x}^{2}=4ay,$$ then

The length of the latus rectum of the parabola $$169 \left[(x-1)^2+(y-3)^2\right]=(5x-12y+17)^2$$ is:

The equation of the circle touching $$x = 0, y = 0$$ and $$x = 4$$ is

Equation of the ellipse in its standard form is $$\displaystyle \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

The radius of the circle with center (0,0) and which passes through (-6,8) is

The equation of circle with its centre at the origin is $$x^2+y^2=r^2$$