Explanation and method to remember all rules of standard hyperbolas

NCERT EXERCISE 11.4 |

In each of the Exercises 1 to 6, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

**Question 1.** \frac{x^2}{16}-\frac{y^2}{9}=1

**Question 2.** \frac{y^2}{9}-\frac{x^2}{27}=1

**Question 3.** 9y^2-4x^2=36

**Question 4.** 16x^2-9y^2=576

**Question 5.** 5y^2-9x^2=36

**Question 6.** 49y^2-16x^2=784

In each of the Exercises 7 to 15, find the equations of the hyperbola satisfying the given conditions.

**Question 7.** Vertices (± 2, 0), foci (± 3, 0)

**Question 8.** Vertices (0, ± 5), foci (0, ± 8)

**Question 9.** Vertices (0, ± 3), foci (0, ± 5)

**Question 10.** Foci (± 5, 0), the transverse axis is of length 8.

**Question 11.** Foci (0, ±13), the conjugate axis is of length 24.

**Question 12.** Foci (\pm 3 \sqrt{5}, 0) , the latus rectum is of length 8.

**Question 13.** Foci (± 4, 0), the latus rectum is of length 12

**Question 14.** vertices (± 7,0), e = \frac{4}{3}

**Question 15.** Foci (0, \pm \sqrt{10}), passing through (2, 3)