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

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Complete the square by separating each hatchet -14x and also 10y in two. Then square each.

-14/2 = -7 and also -7² = 49

10/2 = 5 and also 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 it the square source to discover the radius.

√324 = 18

Option (d) is correct.

Radius of provided equation is 18 units.

Step-by-step explanation:

Given : The equation that circle as

We have to discover the radius of given circle.

Consider the offered equation of one

The typical equation of one with center (h,k) and radius r is offered as

Rewriting in typical form, us have,

Grouping x and also y variables, us have,

Convert x terms to perfect square ax by adding 49 both side, us have,

Simplify, us have,

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

Simplify, we have,

Thus, standard type is

Thus, radius of given equation is 18 units.

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
First, we have to change the basic equation in to standard equation:
The radius is 18, i didnt do the work because i adhered to the exact same proscess ^
X2 + y2 - 14x + 10y = 250x2 -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 = 324Therefore the radius, rr = 324^0.5r = 18

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