Answer:
The point 16+24i is the point satisfying the equation
Hence, Option D is correct.
Step-by-step explanation:
We will find mid-point from end points given.
Mid-point formula: [tex](x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
On substituting the values we will get:
[tex](x,y)=(\frac{-25+15}{2},\frac{-17+25}{2})[/tex]
[tex](x,y)=(-5,4)[/tex]
Now, we have general equation of circle:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
We will find r that is distance from mid-point to end oint using distance formula
[tex]\text{distance formula}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here, [tex]x_1=-5,x_2=-25,y_1=4,y_2=-17[/tex]
On substituting the values we get:
[tex]\text{distance formula}=\sqrt{(-25+5)^2+(-17-4)^2}[/tex]
[tex]\text{distance formula}=\sqrt({20}^2+{21}^2)[/tex]
[tex]\text{distance}=\sqrt{841}[/tex]
Hence, [tex]r^2=841[/tex]
Substituting the values in general equation we get:
[tex](x-(-5))^2+(y-4)^2=841[/tex]
[tex]\Rightarrow(x+5)^2+(y-4)^2=841[tex]
And when we substitute x=16 and y=24 the equation will be satisfied
and a=-5 and b=4
Hence, will lie on the circle
Therefore, option D is correct.
