Question

$A(-3,9)$ and $B(9,-1)$ are the endpoints of the diameter of a circle. The equation for this circle is

• A. $(x-3{)}^2+(y-4{)}^2=61$
• B. $(x-7{)}^2+(y+4{)}^2=269$
• C. $(x+7{)}^2+(y-4{)}^2=61$
• D. $(x+3{)}^2+(y+4{)}^2=169$
• E. $(x+3{)}^2+(y-4{)}^2=25$

Answer 1

The correct option is A $(x-3{)}^2+(y-4{)}^2=61$

If $A(x_1,y_1),B(x_2,y_2)$ are endpoints of diameter then equation of circle is given by

$(x-x_1)(x-x_2)+(y-y_1)(y–y_2)=0$

Given $A=(-3,9),B=(9,-1)$

$(x+3)(x-9)+(y-9)(y+1)=0$

$⟹x^2-6x–27+y^2–8y–9=0$

$(x-3{)}^2–36+(y-4{)}^2–25=0$

$(x-3{)}^2+(y-4{)}^2=61$