Question

WILL GIVE BRAINLIEST!

Answer 1

Answer:

The equation the circle is given by

${\bf 4x}^{\bf 2}+{\bf 4y}^{\bf 2}-{\bf 8x+0y-60}={\bf 0}$

Step-by-step explanation:

The general form of the circle is

$x^2+y^2+Dx+Ey+F=0\hfill (1)$

Given points are (5,0) , (0,4) and (2,4)

Let the points (5,0) , (0,4) and (2,4) be (x_1,y_1) , (x_2,y_2) and (x_3,y_3) respectively

The equation of the circle passes through given points (5,0) , (0,4) and (2,4)

Substituting the point (5,0) in (1)

$(-5)^2+(0)^2+D(5)+E(0)+F=0$

$25-5D+F=0$

$5D-F=25\hfill (2)$

Substituting the point (0,4) in

$(0)^2+(4)^2+D(0)+E(4)+F=0$

$16+4E+F=0$

$4E+F=-16\hfill (3)$

Substituting the point (2,4) in

$(2)^2+(4)^2+D(2)+E(4)+F=0$

$4+16+2D+4E+F=0$

$2D+4E+F=-20\hfill (4)$

By solving the equations (2) ,(3) and(4) we get the values of D,E and F as below

$D=-2$  , $E=0$  and $F=-15$

substituting the values of D,E and F in (1) we get

$x^2+y^2-2x+(0)y-15=0$

Now multiplying the above equation into 4 we get

$4x^2+4y^2-8x+(0)y-60=0$