New Senior Secondary Mathematics (Compulsory) 
       S5 Homework 8: Coordinate Geometry of Circle 
        
       NAME:                             CLASS:              CLASS NO.:           
       HOMEWORK 8: COORDINATE GEOMETRY OF CIRCLE 
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       Q1     Find the area of the region of enclosed by the circle C: x  + y  + 16x – 8y – 20 = 0, in terms of π. 
            
            
            
            
            
            
            
            
            
       Q2  A circle with centre P(7, –2) passes through A(4, 5). 
           (a) Find the equation of the circle. 
           (b) Does B(1, 2) lie inside, outside or on the circle? 
            
            
            
            
            
            
            
            
            
            
            
       Q3  [Challenging, but a useful result. (Optional)] 
           For a circle C : x2 + y2 +Dx+Ey+F =0 and a point P(a,b). 
           Show that if  P  lies outside C, then a2 +b2 +Da+Eb+F >0. 
           (This is a very convenient check to determine whether a given point lies outside a circle or not, try this on 
           Q2.) 
                                   
        
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    New Senior Secondary Mathematics (Compulsory) 
    S5 Homework 8: Coordinate Geometry of Circle 
     
    Q4  A circle cuts the y-axis at A and B such that  AB=8. If the coordinates of the center of the circle are  4,−3 , 
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      find the equation of circle. 
       
       
       
       
       
       
       
       
       
       
       
       
       
       
       
    Q5  In the figure, AB is a chord of the circle  x2 + y2 = 64. M 4,−2  is the mid-point of AB. Find the equation 
                                   (  )
      of the chord AB. 
       
                        
                    
     
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        New Senior Secondary Mathematics (Compulsory) 
        S5 Homework 8: Coordinate Geometry of Circle 
         
        Q6  If the two circles  x2 + y2 = 4 and  x2 + y2 −6x−8y+k =0 touch each other externally, find the value of k. 
              
         
         
         
         
         
         
         
         
         
         
         
         
         
        Q7  The center of a circle is  4,−3 . If the circle passes through the points  P 2,1  and Q 2,b , find the value of 
                                      (     )                                           (   )        (   )
             b. 
              
              
                                        
         
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       New Senior Secondary Mathematics (Compulsory) 
       S5 Homework 8: Coordinate Geometry of Circle 
        
       Q8  In the figure,  P 6,4  is a point on the circle C , and its center C  lies on the x axis. C  intersects the  x axis 
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            at  A and B 8,0 , and intersects the  y  axis at D and E . 
                       (   )
            (a) Find the center and radius of C . 
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            (b) Find the equation of C . 
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            (c) Find the coordinates of  A and D. 
             
                
        
        
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