Analytic Geometry Answers

Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.

How conic sections are generated. From your surrounding give four examples of each of circle, parabola, ellipse and hyperbola. Prepare a list of their different informations.

Base of an equilateral triangle lies along the line 9x+40y-50 and its vertex opposite to the base lies
on the line 9x+40y+32=0. Find the length of the side of the triangle and also find its area.

If the point (x, 3) is equidistant from (3, -2) and (7, 4), find x.

A circle has equation (x-a)^2 +(y-a)^2=a^2 where a is a constant.t. The line y+x-a=0 splits the area of the circle into 2 parts, A1
and A2 where A1>A2. Find the area of A2
giving your answer in the form ((a^2)/b)*(c*pi + d) where b c, and d are integers.

Two circles C1
andC2
both have the coordinate axes as tangents.
equation of C1 is (x-a)^2 + (y-b)^2= 25 where a<0 and b>0 and equation of C2 is (x-c)^2 + (y-d)^2= 16 where c,d>0
C1 touches the x axis at the point A and has its centre at the point B


C2 touches the x axis at the point D and has its centre at the point C

Find the area of the quadrilateral ABCD giving your answer as an exact fraction.

A circle with area (25/9)*pi touches the x-axis at the point (4,0).The point T is the furthest point on the circle from the origin O.Find the length of OT giving your answer as a simplified fraction.

Show that the point A(2,-6,0),B(4,-9,6),C(5,0,2),D(7,-3,8) are concyclic.

I need to clear up something. What's the difference between the midpoint of two coordinates and finding half the distance between the points.

The formula for midpoint is ((x2 + x1)/2 , (y2 + y1)/2)
The formula for distance between two points is √((x2 - x1)^2 + (y2 - y1)^2)