Question

AB (= 10 unit) is diameter of a circle with centre at point P = (x, 0) and point B = (0, y). The relation between x and y is:

Options

• x + y = 10

• x + y = 25

• \(x^2+y^2=5\)

• \(x^2+y^2=25\)

Answer 1

\[\mathbf{x^2+y^2=25}\]

Explanation:

Since (AB) is a diameter, the radius is \[PB=\frac{10}{2}=5\text{ units}.\] Also, \[PB=\sqrt{(x-0)^2+(0-y)^2}=\sqrt{x^2+y^2}.\] Hence, \[x^2+y^2=25.\] Option (iv) is correct.