Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ The equation of the semi-ellipse will be of the form axis Accordingly, 2a = 8 ⇒ a = 4 b = 2 x a y b 2 2 1 2 2 y 0, where a is the semi-major 2 2 x y Therefore, the equation of the semi-ellipse is 1, y 0 ….(1) 16 4 Let A be a point on the major axis such that AB = 1.5 m. Draw AC⊥ OB. OA = (4 â€“ 1.5) m = 2.5 m The x-coordinate of point C is 2.5. On substituting the value of x with 2.5 in equation (1), we obtain 2 2 2.5 y 1 16 4 2 6.25 y 1 16 4 2 6.25 y 41 16 2 9.27 y 4 16 2 y 2.4375 y = 1.56 (approx.) ∴AC = 1.56 m Thus, the height of the arch at a point 1.5 m from one end is approximately 1.56 m. 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 ______________________________________________________________________________ Question 6: A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x- axis. Solution 6: Let AB be the rod making an angle θ with OX and P (x, y) be the point on it such that AP = 3 cm. Then, PB = AB â€“ AP = (12 â€“ 3) cm = 9 cm [AB = 12 cm] From P, draw PQ⊥OY and PR⊥OX. In ΔPBQ, PQ x cos PB 9 In ΔPRA, PR y sin PA 3 2 2 Since, sin cos 1, 2 2 y x 3 9 Or, 2 2 x + 81 1 y = 1 9 Thus, the equation of the locus of point P on the rod is 2 2 x + 81 y = 1 9 Question 7: Find the area of the triangle formed by the lines joining the vertex of the parabola x 2 = 12y to the ends of its latus rectum. Solution 7: The given parabola is x 2 = 12y. On comparing this equation with x 2 = 4ay, we obtain 4a = 12 ⇒ a = 3 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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