Class – XIth St. Line, Circle & Conic _Test Time : 2 hour BOOK - A Test Code : 2009 Name : ……………………………………………….………….. Maximum Marks :120 Batch : ………..……….. Roll No. …………………..…… Please read the instructions carefully. Do not tamper with/mutilate the ORS or the Booklet. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers, and electronic gadgets in any form are not allowed to be carried in side the examination hall. SECTION – A Instructions for questions No. 1 to 40. Each Question has 4 choices (A), (B), (C) and (D) for its answers, out of which only one is correct. For each question you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero mark if no bubble is darkened. In case of bubbling of incorrect answer, minus one (-1) mark will be awarded. SECTION-A Q1 The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is (A.) 2 : 5 (B.) 2 : 3 (C.) 1 : 2 (D.) 3 : 7 Q2 The curve with parametric equations x = α + 5 cos θ, y = β + 4 sin θ (where, θ is parameter) is (A.) an ellipse (B.) a hyperbola (C.) a parabola (D.) None of these Q3 The equation of straight line cutting off an intercept – 2 from y-axis and being equally inclined to the axes are (A.) y = x – 2, y = x – 2 (B.) None of these (C.) y = x + 2, y = x – 2 (D.) y = - x – 2, y = x – 2 S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 1 Class – XIth St. Line, Circle & Conic_Test Q4 The equation of the ellipse whose focus is (1, -1), the directrix of line x – y – 3 = 0 and eccentricity 1/2 is (A.) 7x2 + 2xy + 7y2 + 7 = 0 (B.) 7x2 + 2xy + 7y2 + 10x – 10y – 7 = 0 (C.) None of these (D.) 7x2 + 2xy + 7y2 – 10x + 10y + 7 = 0 Q5 Find the equation of a circle concentric with the circle x2 + y2 – 6x + 12y + 15 = 0 and has double of its area. (B.) x2 + y2 – 6x - 12y + 15 = 0 (A.) x2 + y2 – 6x + 12y + 15 = 0 (C.) None of these (D.) x2 + y2 – 6x + 12y – 15 = 0 Q6 If p and p′ be the perpendicular from the origin upon the straight lines x sec θ + y cosec θ = a and x cos θ - y sin θ = a cos 2θ. Then, 4p2 + p′2 is equal to (A.) a4 (B.) a (C.) a2 (D.) a3 x 2 y2 + = 1 whose foci are S and S′, then PS + PS′ is equal to 16 25 (B.) 10 (C.) 5 (D.) 8 Q7 If P is a point on the ellipse (A.) 7 Q8 Equation of a circle which passes through (3, 6) and touches the axes is (A.) None of these (B.) x2 + y2 – 6x – 6y + 9 = 0 (C.) x2 + y2 – 6x – 6y – 9 = 0 (D.) x2 + y2 + 6x + 6y + 3 = 0 S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 2 Class – XIth St. Line, Circle & Conic_Test Q9 In the adjacent figure, equation of refracted ray is (A.) 3x + y − 3 = 0 (C.) None of these (B.) y = 3x + 1 (D.) y + 3x − 3 = 0 Q10 The distance of the point (3, 5) from the line 2x + 3y – 14 = 0 measured parallel to line x – 2y = 1, is 7 7 (A.) (B.) (C.) (D.) 5 13 13 5 Q11 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. (A.) None of these (B.) x2 + y2 – 2x + 2y = 40 (C.) x2 + y2 - 2x – 2y = 47 (D.) x2 + y2 – 2x + 2y = 47 Q12 Find the equation of a circle which touches both the axes and the line 3x – 4y + 8 = 0 and lies in the third quadrant. (A.) None of these (B.) x2 + y2 + 4x + 4y + 4 = 0 (C.) x2 + y2 - 4x - 4y + 4 = 0 (D.) x2 + y2 + 4x + 4y – 4 = 0 S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 3 Class – XIth St. Line, Circle & Conic_Test Q13 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. (A.) x 2 y2 + =1 81 9 (B.) x 2 y2 − =1 81 9 (C.) x 2 y2 + =1 9 81 (D.) x 2 y2 + =1 9 3 Q14 The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0 at right angle. Find the value of h. 22 22 22 22 (B.) (C.) (D.) (A.) 7 9 13 9 Q15 If the point (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then the equation of the parabola is (B.) x2 + 8y = 32 (C.) x2 + 16y = 30 (D.) x2 + 8y = 16 (A.) x2 – 8y = 32 Q16 Equation of straight line belonging to families of straight lines (x + 2y) + λ(3x + 2y + 1) = 0 and (x – 2y) + μ(x – y + 1) = 0 is (A.) None of these (B.) 6x + 5y = 2 (C.) 5x – 6y + 4 = 0 (D.) 5x + 6y = 4 Q17 A man running a race course notes that sum of its distances from two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man. (A.) x 2 y2 + =1 3 5 (B.) None of these (C.) x 2 y2 + =1 25 9 (D.) x2 y2 + =1 9 25 S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 4 Class – XIth St. Line, Circle & Conic_Test Q18 If the equation of parabola is x2 = - 9y, then equation of directrix and length of latusrectum are (A.) None of these (B.) y = 9/4, 9 (C.) x = 9/4, 9 (D.) y = - 9/4, 8 Q19 A ray of light passing through the point (1, 2) reflects on the X-axis at point A and the reflected ray passes through the point (5, 3). Find coordinates of A. (A.) (13/5, 0) (B.) (- 13/5, 0) (C.) (0, 13/5) (D.) None of these Q20 The area of the circle centred at (1, 2) and passing through (4, 6) is (A.) 25π (B.) 10π (C.) 5π x2 y2 + =1 36 20 (C.) - 18 (D.) None of these Q21 Find the distance between the directrices of the ellipse (A.) 17 (B.) 18 (D.) 19 Q22 The coordinates of a point on the parabola y2 = 8x whose focal distance is 4, is (A.) (1, 4), (2, - 4) (B.) (2, 4), (2, - 4) (C.) (- 2, - 4), (2, (D.) (2, - 4), (- 2, 4) 4) Q23 Find the length of the line segment joining the vertex of the parabola y2 = 4ax and a point on the parabola where the line segment makes an angle θ to the x-axis. 2a cos θ 4a cos θ 4a cos θ (A.) (B.) (C.) None of these (D.) 2 2 sin θ sin θ 3 sin 2 θ Q24 Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line 3 x + y + 2 = 0. (A.) 220º, 3 (B.) 210º, 2 (C.) None of these (D.) 210º, 1 S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 5 Class – XIth St. Line, Circle & Conic_Test Q25 If A(- a, 0) and B(a, 0) are two fixed points, then the locus of the point at which AB subtends a right angle is (B.) x2 + y2 = a2 (A.) x2 + y2 = 2a2 (C.) x2 + y2 + a2 = 0 (D.) x2 – y2 = a2 Q26 An arch is the form of a semi ellipse, It is 8m wide and 2m high of the centre. Find the height of the arch at a point 1.5 m from one end. (A.) None of these (B.) 1.56 m approx (C.) 1.62 m approx (D.) 1.58 m approx Q27 Find the equation of circle with centre (- a, - b) and radius a 2 − b 2 . (B.) x2 + y2 + 2ax + 2by + 2b2 = 0 (A.) x2 + y2 + 2ax + by + 2b2 = 0 (C.) None of these (D.) x2 + y2 – 2ax – 2by – 2b2 = 0 Q28 Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latusrectum. (A.) 18 sq. units (B.) 20 sq. units (C.) 17 sq. units (D.) 19 sq. units Q29 Find the equation of line parallel to Y-axis and drawn through the point of intersection of the line x – 7y + 5 = 0 and 3x + y = 0 (A.) 22x + 5 = 0 (B.) x + 44 = 0 (C.) 22x – 5 = 0 (D.) x + 22 = 0 Q30 Find the equation of the circle which touches the both axes in first quadrant and whose radius is a. (B.) x2 + y2 – 2ax – 2ay + a2 = 0 (A.) x2 + y2 + 2ax – 2ay + a2 = 0 (C.) x2 + y2 – 2ax + 2ay – a2 = 0 (D.) None of these S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 6 Class – XIth St. Line, Circle & Conic_Test Q31 Any point on the hyperbola (A.) (4 sec θ - 4, 2 tan θ - 2) (C.) (4 sec θ, 2 tan θ) ( x + 1) 2 ( y − 2) 2 − = 1 is of the form 16 4 (B.) (4 sec θ - 1, 2 tan θ - 2) (D.) (4 sec θ - 1, 2 tan θ + 2) Q32 Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y – 4x + 3 = 0. (B.) x2 + y2 – 4x + 10y – 25 = 0 (A.) x2 + y2 – 4x – 10y + 25 = 0 (C.) None of these (D.) x2 + y2 – 4x – 10y – 25 = 0 Q33 If the latusrectum of an ellipse is equal to half of minor axis, then its eccentricity is 15 15 15 15 (B.) (C.) (D.) (A.) 6 2 4 3 Q34 If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then find the radius of the circle. (A.) 1/4 (B.) 4/3 (C.) 3/4 (D.) 7/4 Q35 The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is (B.) x2 + y2 = 4a2 (C.) x2 + y2 = a2 (D.) x2 + y2 = 16a2 (A.) x2 + y2 = 9a2 Q36 The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point is (A.) 3 (B.) 4 (C.) 2 (D.) 1 S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 7 Class – XIth St. Line, Circle & Conic_Test Q37 The coordinates of circumcentre of the triangle whose vertices are (- 2, - 3), (- 1, 0), (7, - 6), are (A.) (3, 3) (B.) None of these (C.) (- 3, 3) (D.) (3, - 3) Q38 If a circle passes through the point (0, 0), (a, 0) and (0, b), then find the coordinates of its centre. b⎞ ⎛ a ⎛a b⎞ ⎛ a b⎞ (A.) ⎜ − , − ⎟ (B.) ⎜ , − ⎟ (C.) ⎜ − , ⎟ (D.) None of these 2⎠ ⎝ 2 ⎝2 2⎠ ⎝ 2 2⎠ Q39 Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2). (A.) None of these (B.) x – 7y + 12 = 0, 7x + y + 16 = 0 (C.) x – 7y + 6 = 0, 7x + y – 16 = 0 (D.) x – 7y + 12 = 0, 7x + y – 16 = 0 Q40 If a parabolic reflector is 20 cm in diameter and 5 cm deep, then the focus is (A.) (0, - 5) (B.) (- 5, 0) (C.) (0, 5) (D.) (5, 0) S.C.O. 14 (1st & 2nd Floor), Sector 23-C, Chandigarh - 160023. Ph: 9888228231, 9216338231 www.ssmconline.com, e-mail :[email protected] 8

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