Latus Rectum MCQ Quiz in বাংলা - Objective Question with Answer for Latus Rectum - বিনামূল্যে ডাউনলোড করুন [PDF]
Last updated on Apr 15, 2025
Latest Latus Rectum MCQ Objective Questions
Top Latus Rectum MCQ Objective Questions
Latus Rectum Question 1:
Let the eccentricity of an ellipse
Answer (Detailed Solution Below) 0 - 2
Latus Rectum Question 1 Detailed Solution
Calculation:
Since the curves intersect each other orthogonally
The ellipse and the hyperbola are confocal
⇒
For ellipse aeE = 1
⇒
Length of L.R
Hence, the correct answer is 2.
Latus Rectum Question 2:
Find the eccentricity of the ellipse in which length of minor axis is equal to one-fourth of the distance between their foci.
Answer (Detailed Solution Below)
Latus Rectum Question 2 Detailed Solution
Answer (1)
Sol.
2b =
b2 = a2 - a2e2
b2 = a2 - 16b2
17b2 = a2
e =
Latus Rectum Question 3:
Let the length of a latus rectum of an ellipse
Answer (Detailed Solution Below)
Latus Rectum Question 3 Detailed Solution
Calculation:
Length of LR =
⇒
Min value of
⇒
From (1) & (2)
⇒
∴ a2 + b2 = 81 +45 = 126
Hence, the correct answer is Option 2.
Latus Rectum Question 4:
The length of the latus-rectum of the ellipse, whose foci are (2, 5) and (2, –3) and eccentricity is
Answer (Detailed Solution Below)
Latus Rectum Question 4 Detailed Solution
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.
Latus Rectum Question 5:
What is the sum of the major and minor axes of the ellipse whose eccentricity is 4/5 and length of latus rectum is 14.4 unit?
Answer (Detailed Solution Below)
Latus Rectum Question 5 Detailed Solution
Concept:
Standard equation of an ellipse:
Coordinates of foci = (± ae, 0)
Eccentricity (e) =
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.
Latus Rectum Question 6:
What is the length of the latus rectum of the ellipse 25x2 + 16y2 = 400 ?
Answer (Detailed Solution Below)
Latus Rectum Question 6 Detailed Solution
Concept:
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Equation |
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Length of Latus rectum |
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Calculation:
25x2 + 16y2 = 400
Comparing, with standard equation: a = 4 ; b = 5
Since ( a
Latus Rectum Question 7:
The length of latus rectum of the ellipse 3x2 + y2 -12x + 2y + 1 = 0 is
Answer (Detailed Solution Below)
Latus Rectum Question 7 Detailed Solution
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
∴ a2 = 22 and b2 = (2√3)2
Here a
So, length of latus rectum = 2a2/b
=
=
Hence, option (3) is correct.
Latus Rectum Question 8:
If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity?
Answer (Detailed Solution Below)
Latus Rectum Question 8 Detailed Solution
Concept:
The equation of ellipse is
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
⇒
⇒ e =
If the latus rectum of an ellipse is equal to half of the minor axis, then what is its eccentricity e =
Latus Rectum Question 9:
Let the foci of a hyperbola be (1, 14) and (1, –12). If it passes through the point (1, 6), then the length of its latus-rectum is :
Answer (Detailed Solution Below)
Latus Rectum Question 9 Detailed Solution
Calculation
be = 13, b = 5
a2 = b2 (e2 – 1)
= b2 e2 – b2
= 169 – 25 = 144
Hence option 3 is correct
Latus Rectum Question 10:
Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis. If its eccentricity is
Answer (Detailed Solution Below)
Latus Rectum Question 10 Detailed Solution
The required area is in the shape of kite.
Area of kite
Now,