Analytic Geometry

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

A.   15π C.   169π
B.   13π D.   225π

 

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.

A.   5 C.   3
B.   -3 D.   -5

 

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

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

A.   62.4° C.   42.6°
B.   64.2° D.   46.2°

 

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

A.   $4x + 3y = 0$ C.   $3x + 4y = 0$
B.   $3x - 4y = 0$ D.   $4x - 3y = 0$

 

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

A.   6 C.   4
B.   9 D.   3

 

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

A.   1/2 C.   2/3
B.   2 D.   1.5

 

 
 
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