A circle with centre (4,5) passes through the y-intercept...
A circle with centre (4,5) passes through the y-intercept of the line 5x - 2y + 6 = 0. Find its equation.
x2+y2+8x−10y+21=0
x2+y2+8x−10y−21=0
x2+y2−8x−10y−21=0
x2+y2−8x−10y+21=0
Correct answer is D
On the y-intercept, x=0. At this point, y = 5(0) - 2y = -6; y = 3, so the y- intercept has coordinates (0,3).
The equation of the circle is given as (x−a)2+(y−b)2=r2, where (a,b) is the centre and r is the radius.
The radius of the circle through the y- intercept = √(4−0)2+(5−3)2=√20
The equation of the circle is (x−4)2+(y−5)2=20; expanding, we have
x2+y2+8x−10y+21=0
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