X2 + y2 - 14x + 10y = 250

x2 -14x + 49 - 49 + y2 + 10x + 25 - 25 = 250

(x - 7)^2 - 49 + (y+5)^2 - 25 = 250

(x-7)^2 + (y+5)^2 = 250 + 49 + 25

(x-7)^2 + (y+5)^2 = 324

Therefore the radius, r

r = 324^0.5

r = 18

x2 -14x + 49 - 49 + y2 + 10x + 25 - 25 = 250

(x - 7)^2 - 49 + (y+5)^2 - 25 = 250

(x-7)^2 + (y+5)^2 = 250 + 49 + 25

(x-7)^2 + (y+5)^2 = 324

Therefore the radius, r

r = 324^0.5

r = 18

Equation: x^2 + y^2 − 14x + 10y = 250

1) x^2 − 14x + y^2 + 10y = 250

2) x^2 − 14x + (-14/2)^2 + y^2 + 10y + (10/2)^2 = 250 + (-14/2)^2 + (10/2)^2

3) (x − 7)^2 + (y + 5)^2 = 324

4) (x − 7)^2 + (y + 5)^2 = 18^2

Radius =18 units

1) x^2 − 14x + y^2 + 10y = 250

2) x^2 − 14x + (-14/2)^2 + y^2 + 10y + (10/2)^2 = 250 + (-14/2)^2 + (10/2)^2

3) (x − 7)^2 + (y + 5)^2 = 324

4) (x − 7)^2 + (y + 5)^2 = 18^2

Radius =18 units

Complete the square .

x^2-14x = (x-7)^2-(-7)^2

= (x-7)^2-49

y^2+10y = (x+5)^2-(5)^2

=(x+5)^2-25

(x-7)^2+(y+5)^2-49-25=250

(x-7)^2+(y+5)^2=324

=sqrt 324

=18

x^2-14x = (x-7)^2-(-7)^2

= (x-7)^2-49

y^2+10y = (x+5)^2-(5)^2

=(x+5)^2-25

(x-7)^2+(y+5)^2-49-25=250

(x-7)^2+(y+5)^2=324

=sqrt 324

=18

Option (d) is correct.

Radius of given equation is 18 units.

Step-by-step explanation:

Given : The equation of circle as

We have to find the radius of given circle.

Consider the given equation of circle

The standard equation of circle with center (h,k) and radius r is given as

Rewriting in standard form, we have,

Grouping x and y variables, we have,

Convert x terms to perfect square term by adding 49 both side, we have,

Simplify, we have,

Convert y terms to perfect square term by adding 25 both side, we have,

Simplify, we have,

Thus, standard form is

Thus, radius of given equation is 18 units.

D

Step-by-step explanation:

To find the radius of the circle with equation x2 + y2 – 14x + 10y = 250, convert the equation into vertex-form (x - h)² + (y-k)² = r². Convert by completing the square for x² - 14x and y² + 10y.

Complete the square by dividing each term -14x and 10y in two. Then square each.

-14/2 = -7 and -7² = 49

10/2 = 5 and 5² = 25

The equation becomes x² - 14x + 49 + y² + 10y + 25 = 250 + 49 + 25.

We simplify the equation into (x-7)² + (y + 5)² = 324.

324 is the value of radius squared. Take the square root to find the radius.

√324 = 18

The radius is 18 units.

18

Step-by-step explanation:

x^2 + y^2 – 14x + 10y = 250

x^2 -14x + y^2 + 10y = 250

x^2 - 14x + (-7)^2 + y^2 + 10y + (5)^2 = 250 + (-7)^2 + (5)^2

(x-7)^2 + (y + 5)^2 = 250 + 49 + 25

(x-7)^2 + (y + 5)^2 = 324

Comparing with the general circle (x - b)^2 + (y - a)^2 = r^2

we have; r^2 = 324

r = square root(324)

r = 18

18

Step-by-step explanation:

x^2 + y^2 – 14x + 10y = 250

x^2 -14x + y^2 + 10y = 250

x^2 - 14x + (-7)^2 + y^2 + 10y + (5)^2 = 250 + (-7)^2 + (5)^2

(x-7)^2 + (y + 5)^2 = 250 + 49 + 25

(x-7)^2 + (y + 5)^2 = 324

Comparing with the general circle (x - b)^2 + (y - a)^2 = r^2

we have; r^2 = 324

r = square root(324)

r = 18

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