Question

Question 14 Find the equation for the ellipse that satisfies the given conditions: Ends of major axis, ends of minor axis (±1, 0)

Class X1 - Maths -Conic Sections Page 255

Answer 1

concept : if equation of ellipse is
x²/a² + y²/b² = 1
then major axis is along X - axis and co-ordinate of ends of major axis are ( ±a, 0)
and minor axis is along Y-axis and co-ordinate of the ends of minor axis are ( 0, ±b ).

Here,
ends of major axis ( 0, ± √15) = ( 0, ± b)
hence, b = √15
ends of minor axis ( ±1, 0) = (±a, 0)
hence, a = 1

now, equation of ellipse is
x²/a² + y²/b² = 1
put the values of a² = 1 { ∵a = 1 } and b² = 15 { ∵b = √15} .
x²/1 + y²/15 = 1