M0IITU10 - Conic sections qns

M0IITU10 - Conic sections qns - Conic Sections 1 If the...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is : (A) 1 2 (B) 3 2 (C) 1 4 (D) 3 4 2. The vertices of a hyperbola are at (0, 0) and (10, 0) and one of its foot is at (18, 0) . The equation of the hyperbola is : x y 2 2 25 144 - = 1 ( ) x y - - 5 25 144 2 2 x y 2 2 25 5 144 - - ( ) ( ) ( ) x y - - - 5 25 5 144 2 2 3. If the eccentricities of the hyperbolas x a y b 2 2 2 2 - = 1 & y b x a 2 2 2 2 - = 1 be e & e 1 , then, 1 1 2 1 2 e e + = 1 2 3 None of these 4. If the line y = 2x + c be a tangent to the ellipse, x y 2 2 8 4 + = 1, then c = ± 4 ± 6 ± 1 ± 8 5. The equation of the tangent to the parabola, y = x 2 - x at the point where x = 1, is : y = - x - 1 y = - x + 1 y = x + 1 y = x - 1 6. If the vertex of a parabola be at origin and directrix be, x + 5 = 0, then its latus rectum is : 5 10 20 40 7. The centre of the ellipse, 4x 2 + 9y 2 - 16x - 54y + 61 = 0, is : (1, 3) (2, 3) (3, 2) (3, 1) 8. Latus rectum of ellipse, 2 2 - 8x - 36y + 4 = 0, is : 8 3 4 3 5 3 16 3 9. The locus of the point of intersection of the lines x a y b + = m & x a y b - = 1 m , where m is a paramater, is always : A circle A parabola An ellipse A hyperbola 10. If the chord joining the points, (at 1 2 , 2 at 1 ) and (at 2 2 2 ) of the y 2 = 4ax passes through the focus of the parabola, then : t 1 t 2 = - 1 t 1 t 2 t 1 + t 2 1 t 1 - t 2 11. The focus of the parabola, y 2 = 4y - 4x is : (0, 2) (1, 2) (2, 0) (2, 1) Conic Sections
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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 12. The line l x + my + n = 0 will touch the parabola, if : (A) mn = a l 2 (B) l m = an 2 (C) l n = am 2 (D) l 13. The line, x cos α + y sin α = p will be a tangent to the conic, x a y b 2 2 2 2 + = 1, if : p 2 = a 2 sin 2 α + b 2 cos 2 α p 2 2 2 p 2 = b 2 2 α + a 2 2 α None of these 14. The equation of the tangent to the parabola, y 2 = 4x + 5 parallel to the line y = 2x + 7, is : 2x - y - 3 = 0 - y + 5 = 0 + y + 15. The eccentricity of curve, x 2 - y 2 = 1 is : 1 2 1 2 2 2 16. The equation, 14x 2 - 4xy + 11y 2 - 44x - 8y + 71 = 0 represents : A circle An ellipse A hyperbola A rectangular hyperbola 17. The maximum number of normal that can be drawn from a point to a parabola is : 0 1 2 3 18. The centre of the ellipse, ( ) ( ) x y x y + - + - 2 9 16 2 2 = 1, (0, 0) (1, 1) (1, 0) (0, 1) 19. The point on the parabola, y 2 = 8x at which the normal is inclined at 60º to the x - axis has the co-ordinates : ( 6, - 4 3 ) ( 6, 4 3 ) ( - 6, - 4 3 ) ( - 3 ) 20. The equation of the ellipse whose latus rectum is 8 & whose eccentricity is 1 2 , referred to the principal axes of co-ordinates, is : x y 2 2 18 32 + = 1 x y 2 2 8 9 + x y 2 2 64 32 + x y 2 2 16 24 + 21. The equation of an ellipse whose focus is (- 1, 1), whose directrix is x - y + 3 = 0 and whose eccentricity 1 2 ,
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M0IITU10 - Conic sections qns - Conic Sections 1 If the...

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