Please help ASAP Due very soon

Mathematics

1 answer:

MissTica3 years ago

6 0

Answer:

y = -3/4 + 4

Step-by-step explanation:

use rise over run to find slope

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Equation of circle is: $\mathbf{(x+1)^2+(y-5)^2=28.94}$

Step-by-step explanation:

We need to find an equation of the circle that satisfies the stated conditions. (Give your answer in standard notation.)

Endpoints of a diameter A(−6, 3) and B(4, 7)

The general equation of circle is: $(x-h)^2+(y-k)^2=r^2$

Where r is radius and (h,k) is centre of circle.

Finding centre of circle

The midpoint of diameter is centre of circle.

So, finding midpoint of A(−6, 3) and B(4, 7)

The formula used is: $Midpoint=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

We have x_1=-6, y_1=3, x_2=4, y_2=7

$Midpoint=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\Midpoint=(\frac{-6+4}{2} ,\frac{3+7}{2} )\\Midpoint=(\frac{-2}{2} ,\frac{10}{2} )\\Midpoint=(-1 ,5)$

So, we get Midpoint (x,y)=(-1,5)

Finding radius of circle

Radius of circle can be found by first finding diameter using distance formula and then divide it by 2.

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\Distance=\sqrt{(4-(-6))^2+(7-3)^2} \\Distance=\sqrt{(4+6)^2+(7-3)^2} \\Distance=\sqrt{(10)^2+(4)^2} \\Distance=\sqrt{100+16}\\Distance=\sqrt{116}\\Distance = 10.77$