Conic Sections (Ex – 11.3)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
Question 1.
x2/36 + y2/16 = 1
Solution:
Given equation of ellipse of x2/36 + y2/16 = 1
Clearly, 36 > 16
The equation of ellipse in standard form is
Question 2.
x2/4 + y2/25 = 1
Solution:
Given equation of ellipse is x2/4 + y2/25 = 1
Clearly, 25 > 4
The equation of ellipse in standard form is
Question 3.
x2/16 + y2/9 = 1
Solution:
Given equation of ellipse is x2/16 + y2/9 = 1
Clearly, 16 > 9
The equation of ellipse in standard form is
Question 4.
x2/25 + y2/100 = 1
Solution:
Given equation of ellipse is x2/25 + y2/100 = 1
Clearly, 100 > 25
The equation of ellipse in standard form is
Question 5.
x2/49 + y2/36 = 1
Solution:
Given equation of ellipse is x2/49 + y2/36 = 1
Clearly, 49 > 36
The equation of ellipse in standard form is
Question 6.
x2/16 + y2/9 = 1
Solution:
Given equation of ellipse is x2/16 + y2/9 = 1
Clearly, 400 > 100
The equation of ellipse in standard form is
Question 7.
36x2 + 4y2 = 144
Solution:
Given equation of ellipse is 36x2 + 4y2 = 144
Question 8.
16x2 + y2 = 16
Solution:
Given equation of ellipse is16x2 + y2 = 16
Question 9.
4x2 + 9y2 = 36
Solution:
Given equation of ellipse is 4x2 + 9y2 = 36
In each 0f the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions:
Question 10.
Vertices (±5, 0), foci (±4,0)
Solution:
Clearly, The foci (±4, o) lie on x-axis.
∴ The equation of ellipse is standard form is
Question 11.
Vertices (0, ±13), foci (0, ±5)
Solution:
Clearly, The foci (0, ±5) lie on y-axis.
∴ The equation of ellipse is standard form is
Question 12.
Vertices (±6, 0), foci (±4,0)
Solution:
Clearly, The foci (±4, 0) lie on x-axis.
∴ The equation of ellipse is standard form is
Question 13.
Ends of major axis (±3, 0), ends of minor axis (0, ±2)
Solution:
Since, ends of major axis (±3, 0) lie on x-axis.
∴ The equation of ellipse in standard form
Question 14.
Ends of major axis (0, ±√5), ends of minor axis (±1, 0)
Solution:
Since, ends of major axis (0, ±√5) lie on i-axis.
∴ The equation of ellipse in standard form
Question 15.
Length of major axis 26, foci (±5, 0)
Solution:
Since the foci (±5, 0) lie on x-axis.
∴ The equation of ellipse in standard form
Question 16.
Length of major axis 16, foci (0, ±6)
Solution:
Since the foci (0, ±6) lie on y-axis.
∴ The equation of ellipse in standard form
Question 17.
Foci (±3, 0) a = 4
Solution:
since the foci (±3, 0) on x-axis.
∴ The equation of ellipse in standard form
Question 18.
b = 3, c = 4, center at the origin; foci on the x axis.
Solution:
Since the foci lie on x-axis.
∴ The equation of ellipse in standard form is
Question 19.
Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6)
Solution:
Since the major axis is along y-axis.
∴ The equation of ellipse in standard form
Question 20.
Major axis on the x-axis and passes through the points (4, 3) and (6, 2).
Solution:
Since the major axis is along the x-axis.
∴ The equation of ellipse in standard form is