Latus Rectum MCQ Quiz in मराठी - Objective Question with Answer for Latus Rectum - मोफत PDF डाउनलोड करा

Calculation:

 

Center C = 

Distance between foci: 

⇒ 2c = 

⇒ c = 4

Also e = a/c ⇒ a = c/e = 

Now b² = a² − c² = 25 − 16 = 9, 

⇒ b = 3

Length of latus rectum =  

Hence, the correct answer is Option 4.

Concept:

Standard equation of an ellipse:  (a > b)

Coordinates of foci = (± ae, 0)

Eccentricity (e) =  ⇔ a²e² = a² – b²

Length of latus rectum = 

Length of major axis =2a and Length of minor axis = 2b

Calculation: 

Here,  e = 4/5 =

Squaring both sides, we get

16/25 = 

∴ (b2 / a2) = 1 - 16/25 =  9/25 ....(1)

Latus rectus 2b2 / a = 14.4

⇒ b2 / a = 7.2

Puting above value in (1),

 7.2/ a = 9/25

⇒ a = 20

Now, b2 = 7.2 × 20 = 144

⇒ b = 12

Sum of major and minor axes = 2a + 2b

= 2(20) + 2(12)

= 64 

Hence, option (3) is correct.

Concept:

Calculation:

25x² + 16y² = 400

Comparing, with standard equation: a = 4 ; b = 5

Since ( a

Concept:

Standard Equation of ellipse: 

Length of latus rectum = 2b²/a, when a > b and 2a²/b, when a

Calculation:

3x² + y² -12x + 2y + 1 = 0

⇒ 3(x² - 4x + 4) – 12 + (y² + 2y + 1) = 0

⇒ 3(x – 2)² – 12 + (y + 1)² = 0

⇒ 3(x – 2)² + (y + 1)² = 12

                                  (Divide by 12)

∴ a² = 2² and b² = (2√3)²

Here a

So, length of latus rectum = 2a²/b

= 

=  units

Hence, option (3) is correct.

Concept:

The equation of ellipse is b)\)

length of Latus rectum of ellipse = 

Length of minor axis = 2b.

 eccentricity = 

Calculations:

Given, the latus rectum of an ellipse is equal to half of the minor axis.

Suppose, the equation of ellipse is 

length of Latus rectum of ellipse = 

Length of minor axis = 2b.

Given, the latus rectum of an ellipse is equal to half of the minor axis

⇒ 

⇒ 

If the equation of ellipse is  then eccentricity = 

⇒ 

⇒ e = 

If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity e = 

Calculation

be = 13, b = 5

a² = b² (e² – 1)

= b² e² – b²

= 169 – 25 = 144

Hence option 3 is correct

The required area is in the shape of kite.

Area of kite

Now,

and

so equation of ellipse is

Concept:

Standard equation of an ellipse:  (a > b)

• Coordinates of foci = (± ae, 0)
• Eccentricity (e) =  ⇔ a2e2 = a2 – b2
• Length of Latus rectum = 

Calculation:

Given: 

Compare with the standard equation of an ellipse: 

So, a² = 100 and b² = 75

∴ a = 10

Length of latus rectum =  = 

Concept:

Calculation:

25x² + 16y² = 400

Comparing, with standard equation: a = 4 ; b = 5

Since ( a