Question

F Find an equation for a circle san istying the gve a) Center (-1,4), passes through (3,7) Center (-1,4). passes through (3,7

Answer 1

Answer:

$(x+1)^{2} +(y-4)^{2} =25$

Step-by-step explanation:

In order to find the equation of the circle, first we need to know the circle's general equation, which is:

$(x-h)^{2} +(y-k)^{2} =r^{2}$ where:

(h,k) is the center of the circle and r the radius of the circle.

Because the problem has given the center (-1,4) then h=-1 and k=4.

We need to find now the radius:

Using the distance equation: $distance=\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$ and because we have the center coordinates and an extra point (3,7) we can find the radius as:

$distance=\sqrt{(3-(-1))^{2}+(7-4)^{2}}$

$distance=\sqrt{4^{2}+3^{2}}$

$distance=\sqrt{16+9}$

$distance=\sqrt{25}$

$distance=5$ which means r=5

In conclusion, the equation for the given circle is $(x+1)^{2} +(y-4)^{2} =5^{2}$ which also, can be written as $(x+1)^{2} +(y-4)^{2} =25$