Question

The equation of circle whose diameter lies on 3x + 5y = -7 and 2x - y = 4 which passes through `(-5, 1/2)` is

विकल्प

• x² + y² - 2x + 4y = 149

• x² + y² - 2x + 4y = `149/4`

• x² + y² + 2x - 4y = 149

• x² + y² + 2x - 4y = `149/4`

Answer 1

x² + y² - 2x + 4y = `149/4`

Explanation:

Since the centre always lies on the diameter, Solving 3x +Sy= -7 and 2x - y = 4, we get Co-ordinates of the centre = (1, -2).

The circle passes through `(-5, 1/2)`

∴ `"r"^2 = (1 + 5)^2 + (- 2 - 1/2)^2`

`= 36 + 25/4 = 169/4`

∴ Equation of circle is

(x - 1)² + (y + 2)² = `169/4`

⇒ x² + y² - 2x + 4y = `149/4`