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CBSE Class 11 (Commerce) Straight Lines and Conic Sections — practice questions — page 4

Explore 152 free Straight Lines and Conic Sections questions in CBSE Class 11 (Commerce) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Straight Lines and Conic Sections questions and exercises with answers

Showing questions 91–120 of 152.

An ellipse has vertices (±13, 0) and foci (±5, 0). Its equation isRead the answer and worked solution →An ellipse has semi-major axis 13 and semi-minor axis 12. How far apart are its foci?Read the answer and worked solution →The constant sum of focal distances on an ellipse is always what compared to the distance between the foci?Read the answer and worked solution →A non-degenerate conic with eccentricity exactly 1 is aRead the answer and worked solution →Eccentricity of an ellipse measures how far the ellipse deviates from beingRead the answer and worked solution →How many branches does a hyperbola have?Read the answer and worked solution →A hyperbola is the locus of points where which quantity for two foci is constant?Read the answer and worked solution →The parabola y² = 4ax with a > 0 extends indefinitely into which quadrants?Read the answer and worked solution →Between which limits does the inclination of any line lie?Read the answer and worked solution →What is the inclination of a line parallel to the y-axis?Read the answer and worked solution →If a line has inclination θ, its slope is defined asRead the answer and worked solution →A line makes an inclination of 45° with the positive x-axis. Its slope isRead the answer and worked solution →Find the slope of the line through (3, –2) and (–1, 4).Read the answer and worked solution →Two non-vertical lines are parallel exactly when their slopes areRead the answer and worked solution →The product of the slopes of two perpendicular non-vertical lines isRead the answer and worked solution →A line of slope 2/3 is perpendicular to a line of slopeRead the answer and worked solution →The line through (–2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (x, 24). Find x.Read the answer and worked solution →Three points on one straight line form a triangle whose area isRead the answer and worked solution →Find the area of the triangle with vertices (0, 0), (4, 0) and (0, 6).Read the answer and worked solution →A point divides the segment from A(1, –3) to B(–3, 9) internally in the ratio 1:3. Its coordinates areRead the answer and worked solution →Which French mathematician published La Géométrie in 1637, introducing the equation of a curve?Read the answer and worked solution →The study of geometry using algebra is calledRead the answer and worked solution →A horizontal line lies 5 units above the x-axis. Its equation isRead the answer and worked solution →The line through (–2, 3) parallel to the x-axis has equationRead the answer and worked solution →The point-slope form of a line through (x0, y0) with slope m isRead the answer and worked solution →Find the line through (–2, 3) with slope –4.Read the answer and worked solution →Deriving the two-point form uses the fact that three points on the line areRead the answer and worked solution →The line through (1, –1) and (3, 5) has y-interceptRead the answer and worked solution →The slope-intercept form of a line isRead the answer and worked solution →What is the y-intercept of the line y = 3x – 7?Read the answer and worked solution →

Worked practice questions

An ellipse has vertices (±13, 0) and foci (±5, 0). Its equation is

  1. x²/169 + y²/144 = 1
  2. x²/169 + y²/25 = 1
  3. x²/144 + y²/169 = 1
  4. x²/13 + y²/5 = 1
Show answer and solution

Correct answer: A. x²/169 + y²/144 = 1

With a = 13 and c = 5, b² = 169 - 25 = 144, so x²/169 + y²/144 = 1.

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An ellipse has semi-major axis 13 and semi-minor axis 12. How far apart are its foci?

  1. 25
  2. 2
  3. 10
  4. 5
Show answer and solution

Correct answer: C. 10

Here c = sqrt(169 - 144) = 5, so the foci are 2c = 10 apart.

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The constant sum of focal distances on an ellipse is always what compared to the distance between the foci?

  1. Equal to it
  2. Half of it
  3. Greater than it
  4. Less than it
Show answer and solution

Correct answer: C. Greater than it

The sum equals 2a, which exceeds 2c because a > c for an ellipse.

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