Question

What is the equation of the circle in General Form whose center is at ( 3, -4) and a radius of 5 units?

1. x² + y² - 6x + 8y + 50 = 0
2. x² + y² -6x + 8y - 50 = 0
3. x² + y² - 6x + 8y = 0
4. x² + y² + 6x - 8y = 0

Answer 1

3. x²+y²-6x+8y = 0 is the correct answer.

Explanation:

Let the point P(x,y) be any point at locus of the circumference of the circle,

Let the center be A(3,-4).

now

AP = 5

or,

`\sqrt{(x - 3) ^(2) + (y + 4)^(2) } = 5`

or, (x-3)²+(y+4)² = 25

or, x²-6x+9+y²+8y+16 = 25

or, x²-6x+8y+y² = 25-25

so, x²-6x+8y+y² = 0