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What is the radius of a circle with the equation x2 + y2 – 14x + 10y = 250? A) 9 units B) 12 units C) 15 units D) 18 units

User Mbm
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first, we have to change the General equation in to standard equation:
User Lexicalscope
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Answer:

Option (d) is correct.

Radius of given equation is 18 units.

Explanation:

Given : The equation of circle as
x^2+y^2-14x+10y=250

We have to find the radius of given circle.

Consider the given equation of circle
x^2+y^2-14x+10y=250

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


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

Rewriting in standard form, we have,

Grouping x and y variables, we have,


\left(x^2-14x\right)+\left(y^2+10y\right)=250

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


\left(x^2-14x+49\right)+\left(y^2+10y\right)=250+49

Simplify, we have,


\left(x-7\right)^2+\left(y^2+10y\right)=250+49

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


\left(x-7\right)^2+\left(y^2+10y+25\right)=250+49+25

Simplify, we have,


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

Thus, standard form is


\left(x-7\right)^2+\left(y-\left(-5\right)\right)^2=18^2

Thus, radius of given equation is 18 units.

User BZezzz
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