Question

Answer the following :

Find the equation of circle which passes through the origin and cuts of chords of length 4 and 6 on the positive side of x-axis and y-axis respectively

Answer 1

Let the circle cut the chord of length 4 on X-axis at point A and the chord of length 6 on Y-axis at point B.

∴ the co-ordinates of point A are (4, 0) and co-ordinates of point B are (0, 6).

Since, ∠BOA is a right angle.

∴ AB represents the diameter of the circle

The equation of a circle having (x₁, y₁) and (x₂, y₂) as end points of diameter is given by

(x – x₁) (x – x₂) + (y – y₁) (y – y₂) = 0

Here, x₁ = 4, y₁ = 0, x₂ = 0, y₂ = 6

∴ the required equation of the circle is

(x – 4) (x – 0) + ( y – 0) (y – 6) = 0

∴ x² – 4x + y² – y = 0

∴ x² + y² – 4x – 6y = 0.