*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.**

**Solution:**

Given equation of ellipse of

Clearly, 36 > 16

The equation of ellipse in standard form is

**Question 2.**

**Solution:**

Given equation of ellipse is

Clearly, 25 > 4

The equation of ellipse in standard form is

**Question 3.**

**Solution:**

Given equation of ellipse is

Clearly, 16 > 9

The equation of ellipse in standard form is

**Question 4.**

**Solution:**

Given equation of ellipse is

Clearly, 100 > 25

The equation of ellipse in standard form is

**Question 5.**

**Solution:**

Given equation of ellipse is

Clearly, 49 > 36

The equation of ellipse in standard form is

**Question 6.**

**Solution:**

Given equation of ellipse is

Clearly, 400 > 100

The equation of ellipse in standard form is

**Question 7.**

**36x ^{2} + 4y^{2} = 144**

**Solution:**

Given equation of ellipse is 36x^{2} + 4y^{2} = 144

**Question 8.**

**16x ^{2} + y^{2} = 16**

**Solution:**

Given equation of ellipse is16x^{2} + y^{2} = 16

**Question 9.**

**4x ^{2} + 9y^{2} = 36**

**Solution:**

Given equation of ellipse is4x^{2} + 9y^{2} = 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, ), ends of minor axis (±1, 0)**

**Solution:**

Since, ends of major axis (0, ) 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, centre 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