Question

Question 16 Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

Class X1 - Maths -Conic Sections Page 255

Answer 1

concept : for foci ( 0, ± c) , equation of ellipse will be of the form x²/b² + y²/a² = 1 . where c² = (a² - b²) , and Length of minor axis = 2b .

Here,
Foci ( 0, ± 6 ) = ( 0, ± c)
hence , c = 6
also Length of minor axis = 2b = 16
b = 8
now, c² = a² - b²
6² = a² - 8²
6² + 8² = a²
a² = 36 + 64 = 100

now, equation of ellipse is
x²/b² + y²/a² = 1
put the values of a² = 100 and b² = 64 { ∵ b = 8}
x²/64 + y²/100 = 1 be