Find the equation of a circle having a center that passes through the given point. PLEASE HELP ME!?

Question

The center is (0,0) and the point is (-2,5)

a. x+y=(sq.rt)3
b. x+y=3
c. x^2+y^2=(sqrt)29
d. x^2+y^2=29

Answer 1

The general form of the equation of a circle is
(x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius.
You can automatically eliminate choices a and b, because x and y must both be squared.
Find the square of the distance between (0,0) and (-2,5).
It is 29.
The answer is d.

Answer 2

The general equation of a circle goes as follows;

(x - h)^2 + (y - k)^2 = r^2

In this case, (h,k) is the coordinates of our center, and r is the radius of the circle.

Since (0, 0) are the coordinates of the circle, we just plug this value in for h and k.

[x - 0]^2 + [y - 0]^2 = r^2
x^2 + y^2 = r^2

Now, all we're missing is r; to solve for r, all we have to do is plug in our given point (-2, 5) as x and y.

(-2)^2 + (5)^2 = r^2
4 + 25 = r^2
29 = r^2

We want r^2 and not r, so there's no point in taking the square root of both sides.

Therefore, the equation of our circle is

x^2 + y^2 = 29

Answer 3

The equation for a circle is (x-h)^2 + (y-ok)^2 = r^2 you be attentive to (h,ok) = (4,7) decide the radius. The radius is the gap from the middle to the given factor. r^2 = (3-4)^2 + (-2-7)^2 r^2 = (-a million)^2 + (-9)^2 r^2 = a million + 80 one = 80 two The equation in properly-known style is (x - 4)^2 + (y - 7)^2 = 80 two

Answer 4

The radius of your circle is given by the length of the hypotenuse of the right triangle with leg lengths of 2 and 5, respectively.

=>
r^2 = 4 + 25
r^2=29

The equation of a circle centered at the origin is given as folows:

x^2 + y^2 = r^2

Thus the equation for this circle is:

d. x^2 + y^2 = 29

Answer 5

D

test it:

if x=-2 and y=5

then

x^2 + y^2 = 29
(-2)^2 + (5)^2 = 29
4 + 25 = 29
29 = 29

check!

Answer 6

first you need to find the radius of the circle. in order to do this you will need to fone the distance of point (-2,5) from the origin. we will find the by using the distance formula

d= sqrt ((x2-x1)^2+(y2-y1)^2)
now plug in the two x and y values, let (0,0) represent (x1,y1) and (-2,5) represent (x2,y2)

then

d= sqrt((-2-0)^2+(5-0)^2)
calculate the above equation , this gives us (sqrt) 29

the origin is at (0,0) so the equation is choice c x^2+y^2=(sqrt)29 but it's r^2 so the answer is choice d

Answer 7

well, the general formula is x^2 + y^2 = radius^2, assuming the center is at 0,0
so to find the radius, you can apply the distance formula or pythagorean theorem.
so the radius turns out to be sqrt(29)
so the formula would be D) x^2 + y^2 = sqrt(29)^2 = 29