Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Here, the coefficient of y is negative. Hence, the parabola opens downwards. On comparing this equation with x 2 = - 4ay, we obtain -4a= -16 ⇒ a = 4 ∴Coordinates of the focus = (0, -a) = (0, -4) Since the given equation involves x 2 , the axis of the parabola is the y-axis. Equation of directrix, y= a i.e., y = 4 Length of latus rectum = 4a= 16 Question 5: Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y 2 = 10x Solution 5: The given equation is y 2 = 10x. Here, the coefficient of x is positive. Hence, the parabola opens towards the right. On comparing this equation with y 2 = 4ax, we obtain 5 4a10 a 2 5 ∴Coordinates of the focus = (a, 0) = ,0 2 Since the given equation involves y 2 , the axis of the parabola is the x – axis. Equation of directx, x = -a, i.e., x = - 5 2 Length of latus rectum = 4a = 10 Question 6: Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x 2 = -9y Solution 6: The given equation is x 2 = â€“9y. Here, the coefficient of y is negative. Hence, the parabola opens downwards. On comparing this equation with x 2 = â€“4ay, we obtain 9 4a 9 b 4 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 ______________________________________________________________________________ 9 ∴Coordinates of the focus = (0, -a) = 0, 4 Since the equation involves x 2 , the axis of the parabola is the y-axis. 9 Equation of the directx, y ai.e., y= 4 Length of latus rectum = 4a = 9 Question 7: Find the equation of the parabola that satisfies the following conditions: Focus (6, 0); directrix x = -6 Solution 7: Focus (6, 0); directrix, x= -6 Since the focus lies on the x-axis, the x-axis is the axis of the parabola. Therefore, the equation of the parabola is either of the form y 2 = 4ax or Y 2 = - 4ax. It is also seen that the directrix, x= -6 is to the left of the y-axis, while the focus (6, 0) is to the right of the y-axis. Hence, the parabola is of the form y 2 = 4ax. Here, a = 6 Thus, the equation of the parabola is y 2 = 24x. Question 8: Find the equation of the parabola that satisfies the following conditions: Focus (0, -3); directrix y = 3 Solution 8: Focus = (0, -3); directrix y= 3 Since the focus lies on the y-axis, the y-axis is the axis of the parabola. Therefore, the equation of the parabola is either of the form x 2 = 4ay or X 2 = - 4ay. It is also seen that the directrix, y= 3 is above the x-axis, while the focus (0, -3) is below the x-axis. Hence, the parabola is of the form x 2 = -4ay. Here, a = 3 Thus, the equation of the parabola is x 2 = -12y. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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