About Conic Sections: The Hyperbola:
A hyperbola is the set of all points in a plane such that the absolute value of the difference between two fixed points is constant. The two fixed points are known as the foci.
Test Objectives
- Demonstrate the ability to sketch the graph of a hyperbola
- Demonstrate the ability to write the equation of a hyperbola
#1:
Instructions: Sketch the graph of each, state the foci and vertices.
$$a)\hspace{.2em}\frac{(y + 1)^2}{16}- \frac{(x - 2)^2}{9}=1$$
$$b)\hspace{.2em}\frac{(x - 1)^2}{9}- \frac{(y + 2)^2}{4}=1$$
Watch the Step by Step Video Lesson View the Written Solution
#2:
Instructions: Write each in standard form.
$$a)\hspace{.2em}-4x^2 + 9y^2 - 16x - 126y - 151=0$$
$$b)\hspace{.2em}-x^2 + y^2 + 20x + 8y - 120=0$$
Watch the Step by Step Video Lesson View the Written Solution
#3:
Instructions: Write each in standard form.
$$a)\hspace{.2em}4x^2 - y^2 + 56x - 4y + 92=0$$
$$b)\hspace{.2em}-x^2 + 4y^2 + 2x - 64y + 239=0$$
Watch the Step by Step Video Lesson View the Written Solution
#4:
Instructions: Write each in standard form.
$$a)\hspace{.2em}\text{vertices}: (7, 17), (7, 3)$$ $$\text{foci}: (7, 10 + \sqrt{149}), (7, 10 - \sqrt{149})$$
$$b)\hspace{.2em}\text{vertices}: (21, -9), (-3, -9)$$ $$\text{foci}: (24, -9), (-6, -9)$$
Watch the Step by Step Video Lesson View the Written Solution
#5:
Instructions: Write each in standard form.
$$a)\hspace{.2em}\text{vertices}: (19, -4), (-5, -4)$$ $$\text{foci}: (20, -4), (-6, -4)$$
$$b)\hspace{.2em}\text{vertices}: (-4, 21), (-4, -9)$$ $$\text{foci}: (-4, 23), (-4, -11)$$
Watch the Step by Step Video Lesson View the Written Solution
Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}\text{vertices}: (2, 3), (2, -5)$$ $$\text{foci}: (2, 4), (2, -6)$$
$$b)\hspace{.2em}\text{vertices}: (4, -2), (-2, -2)$$ $$\text{foci}: (1 + \sqrt{13}, -2), (1 - \sqrt{13}, -2)$$
Watch the Step by Step Video Lesson
#2:
Solutions:
$$a)\hspace{.2em}\frac{(y - 7)^2}{64}- \frac{(x + 2)^2}{144}=1$$
$$b)\hspace{.2em}\frac{(y + 4)^2}{36}- \frac{(x - 10)^2}{36}=1$$
Watch the Step by Step Video Lesson
#3:
Solutions:
$$a)\hspace{.2em}\frac{(x + 7)^2}{25}- \frac{(y + 2)^2}{100}=1$$
$$b)\hspace{.2em}\frac{(y - 8)^2}{4}- \frac{(x - 1)^2}{16}=1$$
Watch the Step by Step Video Lesson
#4:
Solutions:
$$a)\hspace{.2em}\frac{(y - 10)^2}{49}- \frac{(x - 7)^2}{100}=1$$
$$b)\hspace{.2em}\frac{(x - 9)^2}{144}- \frac{(y + 9)^2}{81}=1$$
Watch the Step by Step Video Lesson
#5:
Solutions:
$$a)\hspace{.2em}\frac{(x - 7)^2}{144}- \frac{(y + 4)^2}{25}=1$$
$$b)\hspace{.2em}\frac{(y - 6)^2}{225}- \frac{(x + 4)^2}{64}=1$$