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Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Commerce MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions

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Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 1

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway, which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. A supporting wire is also attached to the roadway 18 meter from the middle. (see figure below)

Q. Find the value of a in the standard equation.

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 1
Since A (50, 24) is a point on the parabola.

(50)2 = 4a(24)

⇒ a = 50 x 50/4 x 24 = 625/24

Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 2

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway, which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. A supporting wire is also attached to the roadway 18 meter from the middle. (see figure below)

Q. Find the length of a supporting wire attached to the roadway 18 m from the middle.

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 2
The x-coordinate of point D is 18.

Hence, at x = 18,

6(18)2 = 625y

⇒ y = 6 x 18 x 18 / 625

⇒ y = 3.11 (approx.)

∴ DE = 3.11 m

DF = DE + EF = 3.11 m + 6 m = 9.11 m

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Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 3

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway, which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. A supporting wire is also attached to the roadway 18 meter from the middle. (see figure below)

Q. What are the coordinates of point A?

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 3
Here, AB = 30 m, OC = 6 m, and BC = 100/2 = 50 m

The coordinates of point A are (50, 30 – 6) = (50, 24).

Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 4

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway, which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. A supporting wire is also attached to the roadway 18 meter from the middle. (see figure below)

Q. What is a particular equation of parabola?

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 4
Equation of the parabola,

x = 4 x 625 / 24 × y

or 6x2 = 625y

Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 5

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway, which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. A supporting wire is also attached to the roadway 18 meter from the middle. (see figure below)

Q. What is the standard equation of parabola in this case?

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 5
The equation of the parabola is of the form x2 = 4ay (as it is opening upwards).
Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 6

Rahul is playing with a long string, he hangs the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10 m high and 5 m wide at its base as shown in the following figure:

Q. Find the value of a in the standard equation.

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 6
It can be clearly seen that the parabola passes through point

⇒ a =

Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 7

Rahul is playing with a long string, he hangs the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10 m high and 5 m wide at its base as shown in the following figure:

Q. How wide is it 2 m from the vertex of the parabola?

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 7
Since, the equation of parabola is

x2 = 5 /8y

⇒ AB = (approx.)

= 2.23 m (approx.)

Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 8

Rahul is playing with a long string, he hangs the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10 m high and 5 m wide at its base as shown in the following figure:

Q. Parabola passes through the point:

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 8
It can be clearly seen from the given figure that the parabola passes through point
Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 9

Rahul is playing with a long string, he hangs the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10 m high and 5 m wide at its base as shown in the following figure:

Q. What is a particular equation of parabola?

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 9
he equation of parabola is x2 = 4ay

x2 =

Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 10

Rahul is playing with a long string, he hangs the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10 m high and 5 m wide at its base as shown in the following figure:

Q. What is the standard equation of parabola in this case?

Detailed Solution for Test: Circle, Parabola, Ellipse & Hyperbola- Case Based Type Questions - Question 10
The equation of the parabola is of the form x2 = 4ay (as it opens upwards).
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