# Analytic Geometry

**Problem**

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

A. $y = x^2 + 6x$ | C. $y = x^2 + 4x$ |

B. $y = x^2 - 6x$ | D. $y = x^2 - 4x$ |

**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.

A. $x^2 + y^2 + z^2 - 9 = 0$ |

B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ |

C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ |

D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ |

**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. $4x - 3y = 0$ |