Tiêu đề Ch 11 Conic Sections AR Questions.pdf ✅

Class 11 Maths Chapter 11 Conic Sections Assertion and Reason Questions Directions: Each of these questions contains two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below. (a) Assertion is correct, reason is correct; reason is a correct explanation for assertion. (b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion (c) Assertion is correct, reason is incorrect (d) Assertion is incorrect, reason is correct. 1. Assertion: Length of focal chord of a parabola y 2 = 8x making an angle of 60∘ with x-axis is 32. Reason: Length of focal chord of a parabola y 2 = 4ax making an angle α with x-axis is 4acosec2 α 2. Assertion: If P ( 3√3 2 , 1) is a point on the ellipse 4x 2 + 9y 2 = 36. Circle drawn AP as diameter touches another circle x 2 + y 2 = 9, where A ≡ (−√5, 0) Reason: Circle drawn with focal radius as diameter touches the auxiliary circle. 3. Assertion: Ellipse x 2 25 + y 2 16 = 1 and 12x 2 − 4y 2 = 27 intersect each other at right angle. Reason : Whenever focal conics intersect, they intersect each other orthogonally. 4. Assertion: Centre of the circle x 2 + y 2 − 6x + 4y − 12 = 0 is (3, −2). Reason: The coordinates of the centre of the circle x 2 + y 2 + 2gx + 2fy + c = 0 are (− 1 2 coefficient of x, − 1 2 coefficient of y ) 5. Assertion: Radius of the circle 2x 2 + 2y 2 + 3x + 4y + 9 8 = 0 is 1. Reason: Radius of the circle x 2 + y 2 + 2gx + 2fy + c = 0 is √( 1 2 coeff. of x) 2 + ( 1 2 coeff. of y) 2 − constant term 6. Assertion: Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola. Reason: The equation of a hyperbola with foci on the y-axis is: x 2 a2 − y 2 b2 = 1 7. Assertion: A hyperbola in which a = b is called a rectangular hyperbola. Reason: The eccentricity of a hyperbola is the ratio of the distances from the centre of the hyperbola to one of the foci and to one of the vertices of the hyperbola.
8. Assertion: Eccentricity of conjugate hyperbola is equal to √ b2+a2 b2 Reason: Equation of directrix of conjugate hyperbola is y = ± b e 9. Assertion: The area of the ellipse 2x 2 + 3y 2 = 6 is more than the area of the circle x 2 + y 2 − 2x + 4y + 4 = 0. Reason: The length of semi-major axis of an ellipse is more than the radius of the circle. 10. Parabola is symmetric with respect to the axis of the parabola. Assertion: If the equation has a term y 2 , then the axis of symmetry is along the x-axis. Reason: If the equation has a term x 2 , then the axis of symmetry is along the x-axis. 11. Let the centre of an ellipse is at (0,0) Assertion: If major axis is on the y-axis and ellipse passes through the points (3,2) and (1,6), then the equation of ellipse is x 2 10 + y 2 40 = 1. Reason: x 2 b2 + y 2 a2 = 1 is an equation of ellipse if major axis is along y-axis.
Answers 1. (d) 2. (a) 3. (a) 4. (a) 5. (a) 6. (c) 7. (d) 8. (b) 9. (b) 10. (c) 11. (a)