Homework Soursea find the equation of the circle with radius 10 and centre
(a) find the equation of the circle with radius 10 and centre (2,1), giving your answer in the form x^2+y^2+ax+by+c=0
(b) the circle passes through the point (5,k) where k>0 find the value of k in the form p+sqrt(q)
(c) Determine, showing all working, whether the point (-3,9) lies inside or outside the circle.
(d) find an equation of the tangent to the circle at the point (8,9)
(b) the circle passes through the point (5,k) where k>0 find the value of k in the form p+sqrt(q)
(c) Determine, showing all working, whether the point (-3,9) lies inside or outside the circle.
(d) find an equation of the tangent to the circle at the point (8,9)
Solution
a) (x-2)^2 + (y-1)^2 = 100 => x^2 +y2 - 4x -2y = 95
b) (3)^2 +(k-1)^2 = 100
k-1)^2 = 91
k = 1 +sqrt(91)
c) 5^2 +8^2 - 100 < 0 so inside
d) 2x + 2y* y\' -4 - 2y\' = 0
16 + 16y\' - 4 =0
y\' = -3/4
y-9 = -3/4(x-8)
4y - 36 = -3x + 24
3x+4y = 60
