Sujeet Kumar

Question 1.Find a range of the following data:19, 27, 15, 21, 33, 45, 7, 12, 20, 26Solution:Here, largest value (L) = 45, smallest value (S) = 7∴ Range = L – S = 45 – 7 = 38 Question 2.Find range of the following data:575, 609, 335, 280, 729, 544, 852, 427, 967, 250Solution:Here, largest … Read more

(I) Select the correct option from the given alternatives. Question 1. Question 2.The length of latus rectum of the parabola  – 4x – 8y + 12 = 0 is ________(A) 4(B) 6(C) 8(D) 10Answer:(C) 8Hint:Given equation of parabola is Question 3.If the focus of the parabola is (0, -3), its directrix is y = 3, … Read more

Question 1.Find the length of the transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices, and the length of the latus rectum of the hyperbolae. ⇒ b = 4 and a = 5Length of transverse axis = 2b = 2(4) = 8Length of conjugate axis = 2a = 2(5) … Read more

Question 1.Find the(i) lengths of the principal axes(ii) co-ordinates of the foci(iii) equations of directrices(iv) length of the latus rectum(v) distance between foci(vi) distance between directrices of the ellipse: a = 5 and b = 3Since a > b,X-axis is the major axis and Y-axis is the minor axis. (i) Length of major axis = … Read more

Question 1.Find co-ordinates of focus, equation of directrix, length of latus rectum and the co-ordinates of end points of latus rectum of the parabola: (ii) Given equation of the parabola is  = -20x.Comparing this equation with  = -4ax, we get⇒ 4a = 20⇒ a = 5Co-ordinates of focus are S(-a, 0), i.e., S(-5, 0)Equation of … Read more

(I) Choose the correct alternative. Question 1.Equation of a circle which passes through (3, 6) and touches the axes is Question 2.If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle. Question 3.Find … Read more

Question 1. Question 2. Question 4.7x – 3y – 1 = 0, which is same as the given line.The line 7x – 3y – 1 = 0 touches the given circle at (1, 2). Question 5.

Question 1. Question 2. Question 3.Find the equation of the circle passing through the points (5, 7), (6, 6), and (2, -2).Solution:Let C(h, k) be the centre of the required circle.Since the required circle passes through points A(5, 7), B(6, 6), and D(2, -2),CA = CB = CD = radiusSubstituting k = 3 in (i), … Read more

Question 1.Find the equation of a circle with(i) centre at origin and radius 4.(ii) centre at (-3, -2) and radius 6.(iii) centre at (2, -3) and radius 5.(iv) centre at (-3, -3) passing through point (-3, -6).Solution:(i) The equation of a circle with centre at origin and radius ‘r’ is given by (iv) Centre of … Read more

(I) Select the correct option from the given alternatives. Question 1.If A is (5, -3) and B is a point on the X-axis such that the slope of line AB is -2, then B ≡ Question 2. Question 3.If A(1, -2), B(-2, 3) and C(2, -5) are the vertices of ΔABC, then the equation of … Read more