Question

A circle has a diameter with endpoints at 15 + 25i and –25 – 17i. Which point is also on the circle?

Answer 1

Answer:

The answer is: D, 16+24i!

Answer 2

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: $(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

On substituting the values we will get:

$(x,y)=(\frac{-25+15}{2},\frac{-17+25}{2})$

$(x,y)=(-5,4)$

Now, we have general equation of circle:

$(x-a)^2+(y-b)^2=r^2$

We will find r that is distance from mid-point to end oint using distance formula

$\text{distance formula}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here, $x_1=-5,x_2=-25,y_1=4,y_2=-17$

On substituting the values we get:

$\text{distance formula}=\sqrt{(-25+5)^2+(-17-4)^2}$

$\text{distance formula}=\sqrt({20}^2+{21}^2)$

$\text{distance}=\sqrt{841}$

Hence, $r^2=841$

Substituting the values in general equation we get:

$(x-(-5))^2+(y-4)^2=841$

[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.