Answer:
Option (d) is correct.
Radius of given equation is 18 units.
Step-by-step explanation:
Given : The equation of circle as [tex]x^2+y^2-14x+10y=250[/tex]
We have to find the radius of given circle.
Consider the given equation of circle [tex]x^2+y^2-14x+10y=250[/tex]
The standard equation of circle with center (h,k) and radius r is given as
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Rewriting in standard form, we have,
Grouping x and y variables, we have,
[tex]\left(x^2-14x\right)+\left(y^2+10y\right)=250[/tex]
Convert x terms to perfect square term by adding 49 both side, we have,
[tex]\left(x^2-14x+49\right)+\left(y^2+10y\right)=250+49[/tex]
Simplify, we have,
[tex]\left(x-7\right)^2+\left(y^2+10y\right)=250+49[/tex]
Convert y terms to perfect square term by adding 25 both side, we have,
[tex]\left(x-7\right)^2+\left(y^2+10y+25\right)=250+49+25[/tex]
Simplify, we have,
[tex]\left(x-7\right)^2+\left(y+5\right)^2=324[/tex]
Thus, standard form is
[tex]\left(x-7\right)^2+\left(y-\left(-5\right)\right)^2=18^2[/tex]
Thus, radius of given equation is 18 units.
