Question
Mathematics Question on Straight lines
A circle with center (4,−5) is tangent to the y -axis in the standard (x,y) coordinate plane. What is the radius of this circle?
A
(A) 4
B
(B) 5
C
(C) 41
D
(D) 16
Answer
(A) 4
Explanation
Solution
Explanation:
Equation of circle with center at (h,k) and radius r units is given by: (x−h)2+(y−k)2=r2Here (h,k)=(4,−5) and let the radius be r units.The equation of the required circle is: (x−4)2+(y+5)2=r2.∵y -axis is the tangent to the circle (x−4)2+(y+5)2=r2. So the co-ordinates of the point common to circle (x−4)2+(y+5)2=r2 and the tangent y -axis is (0,−5).∴ The point (0,−5) will satisfy the equation of circle.⇒(0−4)2+(−5+5)2=r2⇒r=4So, the radius of the circle is 4 units.Hence, the correct option is (A).