Analytic Geometry

Problem
Find the Cartesian equation of the curve represented by $x = 4t + 3$ and $y = 16t^2 - 9$, -∞ < t < +∞.

Problem
Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.

Problem
Calculate the area enclosed by the curve $x^2 + y^2 - 10x + 4y - 196 = 0$.

Problem
A circle has an equation of $x^2 + y^2 + 2cy = 0$. Find the value of $c$ when the length of the tangent from (5, 4) to the circle is equal to one.

Problem
Calculate the acute angle between two intersecting surfaces whose equations are as follows:
$$2x - 4y - z = -5$$

$$3x + 4y + 5z = -6$$

Problem
What is the equation of the normal to the curve $x^2 + y^2 = 25$ at (4, 3)?

Problem
What is the radius of the circle $x^2 + y^2 - 6x = 0$?

Problem
Find the distance from the point A(1, 5, -3) to the plane 4x + y + 8z + 33 = 0.