Maths-
General
Easy

Question

The equations x = a costheta  , y = a sintheta, represent

  1. an ellipse    
  2. a parabola    
  3. a circle    
  4. a hyperbola.    

Hint:

The standard equation of a circle is given by:
left parenthesis x minus h right parenthesis squared space plus space left parenthesis y minus k right parenthesis squared space equals space r squared
Where (h,k) is the coordinates of center of the circle and r is the radius.

The correct answer is: a circle


    Given :  x = a costheta ------ (1) ,
    y = a sintheta ------ (2)
    Squaring both equations and adding them we get
    rightwards double arrow x squared space plus space y squared space equals space a squared cos squared theta space plus space a squared sin squared theta space
rightwards double arrow x squared space plus space y squared space equals space a squared left parenthesis cos squared theta space plus space sin squared theta space right parenthesis
rightwards double arrow x squared space plus space y squared space equals space a squared space minus negative negative negative negative negative negative negative space left parenthesis 3 right parenthesis

    The standard equation of a circle is given by:
    left parenthesis x minus h right parenthesis squared space plus space left parenthesis y minus k right parenthesis squared space equals space r squared
    Comparing with equation 3
    rightwards double arrow left parenthesis x space minus 0 right parenthesis squared space plus space left parenthesis y space minus space 0 right parenthesis squared space equals a squared comma space h space equals space 0 comma space k space equals space 0 space a n d space r space equals space a squared
    Thus, the equations x = a costheta  , y = a sintheta, , represent a circle.

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