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

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.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for