Find Length of Segment AB in Circle Co-ordinate Question

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SUMMARY

The discussion centers on calculating the length of segment AB formed by a straight line at coordinates c(-81/2, -81/2) making a 135-degree angle with the x-axis, intersecting the circle defined by the parametric equations x=5cos(m) and y=5sin(m). The initial attempt to derive the equation of the line resulted in y=-x, leading to a calculated length of AB as 0. However, the correct approach involves understanding the intersection points of the line and the circle, which requires a different method to arrive at the accurate length of segment AB.

PREREQUISITES
  • Understanding of parametric equations, specifically x=5cos(m) and y=5sin(m).
  • Knowledge of coordinate geometry, particularly the concept of lines and angles in the Cartesian plane.
  • Familiarity with trigonometric functions and their applications in geometry.
  • Ability to solve equations involving intersections of lines and curves.
NEXT STEPS
  • Study the derivation of parametric equations and their geometric interpretations.
  • Learn how to find intersection points between a line and a circle using algebraic methods.
  • Explore the concept of angle measurement in the Cartesian coordinate system.
  • Practice solving problems involving lengths of segments formed by intersecting geometric shapes.
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Mathematics students, geometry enthusiasts, and educators looking to deepen their understanding of coordinate geometry and trigonometric applications in solving intersection problems.

anmolnanda
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the question:
if a straight line c(-*81/2,-*81/2) making an angle 135 dge with x-axis,cuts the circle x=5cosm y=5sinm in points A and B ,find length of segment AB .
in the equation of line by solving i got y=-x
and tried to solve and ended up getting length of AB as 0 but the solution has done a different way and got different answer//probably i am using some wrong concepts..please help
 
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hi anmolnanda! :smile:

(have a square-root: √ and a degree: ° :wink:)
anmolnanda said:
the question:
if a straight line c(-*81/2,-*81/2) making an angle 135 dge with x-axis,cuts the circle x=5cosm y=5sinm in points A and B ,find length of segment AB .

i don't understand …

what does that point have to do with it? :confused:

what exactly is the question?​
 

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