Question

15. Find the length of the chord
Max
a-y-3 = 0 of the circle x + y = x+3y – 225 0 [March 18AP, 13, May 16AP, 111
ii) 3x – y + 4 = 0 of the circle x'+y + 8x - 4y - 16 = 0
iii) x cos a + y sin a =p of the circle x² + y2 = a? [May 16TS]​

Answer 1

Answer:

Complete the squares: x^2-8x+16+y^2+4y+4-4=0⇒(x-4)^2+(y+2)^2=4. This form of the equation tells us where the centre of the circle is and what the radius is. The centre is where x-4=0, so x=4, and where y+2=0, so y=-2. The constant on the right is the square of the radius. This constant was the result of completing the squares by providing the right constant, and adjusting the original constant, 16, so 16 was changed to 16-16-4=-4, which became 4 when moved to the right hand side. The centre of the circle is at (4,-2) and the radius is sqrt(4)=2. Because we know where the centre is we know that if we move a radius to the right and left we get the diameter. So the diameter goes from (2,-2) to (6,-2) horizontally; and from (4,-4) to (4,0) vertically. These parameters help to draw the circle, perhaps with the help of a pair of compasses.