find the equation of circles passing through (0,0)and which makes intercepts a and b on the coordinate axis
Answers
Answered by
3
Let the center be C(h,k).
Let the circle cut the X axis at A and the Y axis at B.
Let the circle make an intercept of length b on X axis so the coordinates of A are (b,0). Similarly, intercept of length a is made on Y axis. Hence the coordinates of B is (0,a).
(h-0)²+(k-0)²=(h-0)²+(k-a)²
h²+k²=h²+k²+a²-2ka
2ka=a²
k=a/2
(h-0)²+(k-0)²=(h-b)²+(k-0)²
h²+k²=h²+k²+a²-2hb
2hb=b²
h=b/2.
(Radius)²=(a/2)²+(b/2)²=(a²+b²)/4
Equation is (x-b/2)²+(y-a/2)=(a²+b²)/4
On solving we get
x²+y²-bx-ay=0
Let the circle cut the X axis at A and the Y axis at B.
Let the circle make an intercept of length b on X axis so the coordinates of A are (b,0). Similarly, intercept of length a is made on Y axis. Hence the coordinates of B is (0,a).
(h-0)²+(k-0)²=(h-0)²+(k-a)²
h²+k²=h²+k²+a²-2ka
2ka=a²
k=a/2
(h-0)²+(k-0)²=(h-b)²+(k-0)²
h²+k²=h²+k²+a²-2hb
2hb=b²
h=b/2.
(Radius)²=(a/2)²+(b/2)²=(a²+b²)/4
Equation is (x-b/2)²+(y-a/2)=(a²+b²)/4
On solving we get
x²+y²-bx-ay=0
Similar questions