Question

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

Answer 1

D

Explanation:

edge :)

Answer 2

The point 16+24i is the point satisfying the equation

Hence, Option D is correct.

Explanation:

We will find mid-point from end points given.

Mid-point formula:
`(x,y)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

On substituting the values we will get:

`(x,y)=((-25+15)/(2),(-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}=√((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}=√((-25+5)^2+(-17-4)^2)`

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

`\text{distance}=√(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.