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Match the items of Column I with those of Column II.Column IColumn II(A) Equation of the line with x-intercept 4 and passing through the point (2, 3) is(p) x + 4y - 8 = 0(B) Equation of the line passing through (4, 1) and forming a triangle with positive coordinate axes whose area is 8 sq. unit is(q) 3x - 2y = 12C) Equation of the line with equal intercepts on the axes and is passing through the point (2, 5) is(r) x + y = 7 = 0(D) Equation of the line which makes an angle of 135° with the positive direction of the axis and makes an intercept of 8 on y-axis is(s) 2x + y + 1= 0(t) x + y - 8 = 0 |
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Answer» Equation of the line is x/4 + y/b = 1 It passes through (2, 3). This implies that 2/4 + -3/b = 1 ⇒ -3/b = 1/2 ⇒ b = -6 Hence, the equation of the line is x/4 - y/6 = 1 3x - 2y = 12= 0 Answer: (A) → (q) (B) Let x/a + y/b = 1 It passes through (4, 1) and forms a triangle with positive axes having area 8. Therefore 4/a + 1/b = 1 ...(1) and 1/2(ab) = 8 From Eqs. (1) and (2), a = 8 and b = 2. Hence, the equation of the line is x/8 + y/2 = 1 or x + 4y - 8 = 0 Answer: (B) → (p) (C) Equation of the line with equal intercepts on the axes is x/a + y/a = 1 or x + y = a This passes through the point (2, 5) implies that a = 7. Hence, the line is x + y - 7 = 0 Answer: (C) → (r) (D) Let the line be y = (tan 135°)x + c where c = 8. That is, y = -x + 8 or x + y = 0. Answer: (D) → (t) |
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