Find the equation of a circle with a point at ( 10 , - 4 ) and a point at ( -2 , - 4 )​

Solution given:

letA=(10,-4)

B=(-2,-4)

centre[C](h,k)=

radius=units

we have

Equation of a circle is;

(x-h)²+(y-k)²=r²

(x-4)²+(y+4)²=36

or.

x²-8x+16+y²+8y+16=36

x²-8x+8y+y²=36-32

x²-8x+8y+y²=4

The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.

Step-by-step explanation:

the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter

since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle

remember midpoint formula,

let,

thus substitute:

simplify addition:

simplify division:

so the centre of the circle is (4,-4)

since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is

simplify which yields:

recall the equation of circle

we acquire that,

therefore substitute:

simplify:

and we are done!

also refer the attachment

(the graph is web resource of desmos)

true

step-by-step explanation:

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