A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find the equation of the hyperbola satisfying the given conditions: Foci (± 3√5, 0), the latus rectum is of length 8
Solution:
Foci (± 3√5, 0),
the latus rectum is of length 8.
Here, the foci are on the x-axis.
Therefore,
the equation of the hyperbola is of the form x2/a2 - y2/b2 = 1
Since the foci are (± 3√5, 0), c = ± 3√5
Since the length of latus rectum is 8,
Then,
⇒ 2b2/a = 24
⇒ b2 = 4a
We know that, c2 = a2 + b2
Hence,
⇒ a2 + 4a = 45
⇒ a2 + 4a - 45 = 0
⇒ a2 + 9a - 5a - 45 = 0
⇒ a (a + 9) - 5(a + 9) = 0
⇒ (a + 9)(a - 5) = 0
⇒ a = - 9, 5
Since a is non-negative, a = 5
Therefore,
⇒ b2 = 4a
⇒ b2 = 4 x 5
⇒ b2 = 20
Thus, the equation of the hyperbola is x2/25 - y2/20 = 1
NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.4 Question 12
Find the equation of the hyperbola satisfying the given conditions: Foci (± 3√5, 0), the latus rectum is of length 8
Summary:
The equation of the hyperbola is x2/25 - y2/20 = 1 while the Foci is (± 3√5, 0) and the latus rectum is of length 8
Math worksheets and
visual curriculum
visual curriculum