Which of the following equations belongs to a circle satisfy

Which of the following equations belongs to a circle satisfying the given conditions: The circle is tangent to the x-axis and to the y-axis. Its center is in the 2nd quadrant. Its diameter is 8 units long. a) x^2 + y^2 + 8x - 8y - 16 = 0 b) x^2 + y^2 + 16x - 16 y + 16 = 0 c) x^2 + y^2 + 8x - 8y -64 = 0 d) x^2 + y^2 + 8x - 8y + 16 = 0 e) x^2 + y^2 - 8x - 8y + 16 = 0 f) None of these

Solution

Tangent to x axis and y axis in IInd quadrant

So, centre (h, k) will have h as -ve and k as +ve

radius = 4 units

standard equation : (x +h)^2 + (y - k)^2 = r^2

x^2 + h^2 +2hx + y^2 + k^2 -2yk - r^2 =0

So, comparing the options : 2hx = 8x ; -2yk = -8y

r^2 = 16

Option A