Question

If y = 2x is a chord of the circle S ≡ x² + y² - 10x = 0, then the equation of the circle described on this chord as diameter is

(A)  x² + y² -  2x -  4y = 0

(B)  x² + y² -  14x +  2y = 0 

(C)  x² + y² -  6x -  2y = 0 

(d)  x² + y² -  18x + 14y = 0

Answer 1

Correct option (A)  x² + y² -  2x -  4y = 0

Explanation :

The required circle of the form S + λ(2x -   y) = 0 is

x² + y² -10x + λ(2x - y) = 0

For this circle, the chord y = 2x is a diameter and if the center of this circle lies on y = 2x, then

Therefore, the required circle is x² + y² - 2x - 4y = 0