Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Miscellaneous Exercise Question 1: If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus. Solution 1: The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that the axis of the reflector is along the positive x-axis. This can be diagrammatically represented as The equation of the parabola is of the form y 2 = 4ax (as it is opening to the right). Since the parabola passes through point A (10, 5), 10 2 = 4a(5) ⇒ 100 = 20a ⇒ a = 100 20 = 5 Therefore, the focus of the parabola is (a, 0) = (5, 0), which is the mid-point of the diameter. Hence, the focus of the reflector is at the mid-point of the diameter. Question 2: If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus. Solution 2: The origin of the coordinate plane is taken at the vertex of the parabolic reflector in such a way that the axis of the reflector is along the positive x-axis. This can be diagrammatically represented as Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ The equation of the parabola is of the form y 2 = 4ax (as it is opening to the right). Since the parabola passes through point A (5, 10), 10 2 = 4a(5) ⇒ 100 = 20a ⇒ a = 100 20 = 5 Therefore, the focus of the parabola is (a, 0) = (5, 0), which is the mid-point of the diameter. Hence, the focus of the reflector is at the mid-point of the diameter. Question 3: An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola? Solution 3: The origin of the coordinate plane is taken at the vertex of the arch in such a way that its vertical axis is along the positive y-axis. This can be diagrammatically represented as The equation of the parabola is of the form x 2 = 4ay (as it is opening upwards). Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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