Advertisements
Advertisements
Question
Find the equation for the ellipse that satisfies the given conditions:
Length of minor axis 16, foci (0, ±6)
Advertisements
Solution
Length of minor axis = 16; foci = (0, ±6).
Since the foci are on the y-axis, the major axis is along the y-axis.
Therefore, the equation of the ellipse will be of the form `x^2/b^2 + y^2/a^2 = 1` where a is the semi-major axis.
Accordingly, 2b = 16 = b = 8 and c = 6
It is known that a2 = b2 + c2
∴ a2 = 82 + 62 = 64 + 36 = 100
= a = `sqrt100` = 10
Thus, the equation of the ellipse is `x^2/8^2 + y^2/10^2 = 1` or `x^2/64 + y^2/100 = 1`.
APPEARS IN
RELATED QUESTIONS
Find the equation for the ellipse that satisfies the given conditions:
Vertices (0, ±13), foci (0, ±5)
Find the equation for the ellipse that satisfies the given conditions:
Vertices (±6, 0), foci (±4, 0)
Find the equation for the ellipse that satisfies the given conditions:
Ends of major axis (±3, 0), ends of minor axis (0, ±2)
Find the equation for the ellipse that satisfies the given conditions:
Ends of major axis (0, `+- sqrt5`), ends of minor axis (±1, 0)
Find the equation for the ellipse that satisfies the given conditions:
Length of major axis 26, foci (±5, 0)
Find the equation for the ellipse that satisfies the given conditions:
b = 3, c = 4, centre at the origin; foci on the x axis.
Find the equation for the ellipse that satisfies the given conditions:
Major axis on the x-axis and passes through the points (4, 3) and (6, 2).
A man running a racecourse notes that the sum of the distances from the two flag posts form him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.
Find the equation of the ellipse in the case:
focus is (0, 1), directrix is x + y = 0 and e = \[\frac{1}{2}\] .
Find the equation of the ellipse in the case:
focus is (−1, 1), directrix is x − y + 3 = 0 and e = \[\frac{1}{2}\]
Find the equation of the ellipse in the case:
focus is (−2, 3), directrix is 2x + 3y + 4 = 0 and e = \[\frac{4}{5}\]
Find the equation of the ellipse in the case:
eccentricity e = \[\frac{1}{2}\] and foci (± 2, 0)
Find the equation of the ellipse in the case:
eccentricity e = \[\frac{1}{2}\] and semi-major axis = 4
Find the equation of the ellipse in the case:
eccentricity e = \[\frac{1}{2}\] and major axis = 12
Find the equation of the ellipse in the case:
The ellipse passes through (1, 4) and (−6, 1).
Find the equation of the ellipse in the case:
Vertices (± 5, 0), foci (± 4, 0)
Find the equation of the ellipse in the following case:
Vertices (± 6, 0), foci (± 4, 0)
Find the equation of the ellipse in the following case:
Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)
Find the equation of the ellipse in the following case:
Ends of major axis (0, ±\[\sqrt{5}\] ends of minor axis (± 1, 0)
Find the equation of the ellipse in the following case:
Length of minor axis 16 foci (0, ± 6)
Find the equation of the ellipse in the following case:
Foci (± 3, 0), a = 4
A bar of given length moves with its extremities on two fixed straight lines at right angles. Any point of the bar describes an ellipse.
The line 2x + 3y = 12 touches the ellipse `x^2/9 + y^2/4` = 2 at the point (3, 2).
An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the length of the string and distance between the pins are ______.
The equation of the ellipse having foci (0, 1), (0, –1) and minor axis of length 1 is ______.
