Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Question 15: Does the point (-2.5, 3.5) lie inside, outside or on the circle x 2 + y 2 = 25? Solution 15: The equation of the given circle is x 2 + y 2 = 25. X 2 + y 2 = 25 ⇒ (x â€“ 0) 2 + (y â€“ 0) = 5 2 , which is of the form (x â€“ h) 2 + (y â€“ k) 2 = r 2 , where h = 0, k = 0, and r = 5. ∴Centre = (0, 0) and radius = 5 Distance between point (â€“2.5, 3.5) and centre (0, 0) 2.5 0 3.5 0 6.25 12.25 18.5 4.3 approx. 5 2 2 Since the distance between point (â€“2.5, 3.5) and centre (0, 0) of the circle is less than the radius of the circle, point (â€“2.5, 3.5) lies inside the circle. Exercise **11**.2 Question 1: Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y 2 = 12x Solution 1: The given equation is y 2 = 12x. Here, the coefficient of x is positive. Hence, the parabola opens towards the right. On comparing this equation with y 2 = 4ax, we obtain 4a= 12 ⇒ a = 3 ∴Coordinates of the focus = (a, 0) = (3, 0) Since the given equation involves y 2 , the axis of the parabola is the x-axis. Equation of direcctrix, x= -a i.e., x = - 3 i.e., x+ 3 = 0 Length of latus rectum = 4a= 4 x 3 = 12 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 2: Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x 2 = 6y Solution 2: The given equation is x 2 = 6y. Here, the coefficient of y is positive. Hence, the parabola opens upwards. On comparing this equation with x 2 = 4ay, we obtain 3 4a 6 a 2 3 ∴Coordinates of the focus = (0, a) = 0, 2 Since the given equation involves x 2 , the axis of the parabola is the y-axis. 3 Equation of directrix, y ai.e., y=- 2 Length of latus rectum = 4a= 6 Question 3: Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y 2 = - 8x Solution 3: The given equation is y 2 = -8x. Here, the coefficient of x is negative. Hence, the parabola opens towards the left. On comparing this equation with y 2 = -4ax, we obtain -4a= -8 ⇒ a = 2 ∴Coordinates of the focus = (-a, 0) = (-2, 0) Since the given equation involves y 2 , the axis of the parabola is the x-axis. Equation of directrix, x= a i.e., x = 2 Length of latus rectum = 4a= 8 Question 4: Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x 2 = - 16y Solution 4: The given equation is x 2 = -16y. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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