Comparing equation with y²=-4ax.
4a=100 => a=25. Directrix is a line parallel to latus rectum in such a way that vertex is at middle of both.
Equation of directrix is x=a => x=25.

Given, a=5 and c=3 => b²=a²-c² = 5²-3²=4² => b=4.
Equation of ellipse with major axis along y-axis is \((\frac{x}{b})^2+(\frac{y}{a})^2\)=1.
So, equation of given ellipse is \((\frac{x}{4})^2+(\frac{y}{5})^2\)=1.

Comparing equation with \((\frac{x}{a})^2+(\frac{y}{b})^2\)=1, we get a=5 and b=4.
Major axis length = 2a = 2*5 =10 units.

Since vertex is at (1, 2) and focus (2, 0) so parabola equation will be
(y-2)²=4*2(x-1)
y²-8x-4y+12=0.

Comparing equation with y²=-4ax.
4a=100 => a=25. Line passing through focus perpendicular to axis is latus rectum.
Equation of latus rectum is x=-a => x=-25.

Given, 2a=8 => a=4 and 2b=10 => b=5.
Equation of hyperbola with transverse axis along x-axis is \((\frac{x}{4})^2-(\frac{y}{5})^2\)=1.
So, equation of given hyperbola is \((\frac{x}{4})^2-(\frac{y}{5})^2\)=1.

Comparing equation with \((\frac{x}{a})^2+(\frac{y}{b})^2\)=1, we get a=5 and b=4.
Minor axis length = 2b = 2*4 = 8 units.

Equation of circle with center at x-axis (a, 0) and radius r units is
(x-a)²+(y)²=r²
=>(2-a)²+(0)²=r²
And (0-a)²+(4)²=r²
=>(a-2)²=a²+4² => (-2)(2a-2) =16 => a-1=-4 => a=-3
So, r² = (2+3)²=5²
r=5 units.

Vertex is close end point of parabola i.e. origin (0, 0) as it satisfies equation (y-0)²=4a(x-0) also.

Comparing equation with x²=4ay.
4a=100 => a=25.
Focus is at (0, a) i.e. (0, 25).