Question

A circle has a diameter with endpoints (-7, 1) and (-3, 7).

What is the equation of the circle?

r2 = ( x - 3) 2 + ( y + 4) 2
r2 = ( x + 3) 2 + ( y - 4) 2
r2 = ( x + 5) 2 + ( y - 4) 2
r2 = ( x - 5) 2 + ( y + 4) 2

Answer 1

Answer: (C) r² = (x+5)²+(y-4)²

Solution:-

The given endpoints are (-7,1) and (-3,7)

so the center will be at the mid point of the line connecting these two points.

hence, center ={ (-7+-3)/2, (1+7)/2 }

hence, C= (-5,4)

so, the equation of the circle is:-

⇒ (x-(-5))²+(y-4)²=r²

or, (x+5)²+(y-4)²=r²