Question

What’s the correct answer for this question?

Answer 1

The circle with center (-1,1) is

(x - -1)² + (y - 1)² = r²

(x + 1)² + (y - 1)² = r²

where r is the unknown radius.

(4,2) is on the circle so

(4 + 1)² + (2 - 1)² = r²

So is (-5, -3)

(-5 + 1)² + (-3 - 1)² = r²

Those are equal so our answer is

Answer: A. (4 + 1)² + (2 - 1)² = (-5 + 1)² + (-3 - 1)²

Answer 2

A.

Explanation:

The equation of circle with center (-1,1) is

(x+1)+(x-1) = r²

Since r² is unknown, We'll find it out by distance formula by point (4,2)

r² = (4+1)²+(2-1)

For point (-5,-3) lying on the circle, it's distance should be equal to the above r²

But the distance isn't equal and

(4+1)²+(2-1)² ≠ (-5+1)²+(-3-1)² So Point (-5,-3) is not on the circle