What is the standard form of the equation of a circle with center at (-3, 1) and through the point (2, 13)?

Answer 1

#(x+3)^2+(y-1)^2=13^2#
(see below for discussion of alternate "standard form")

The "standard form of an equation for a circle" is #color(white)("XXX")(x-a)^2+(y-b)^2=r^2# for a circle with center #(a,b)# and radius #r#
Since we are given the center, we only need to compute the radius (using the Pythagorean Theorem) #color(white)("XXX")r=sqrt((-3-2)^2+(1-13)^2) = sqrt(5^2+12^2) = 13# So the equation of the circle is #color(white)("XXX")(x-(-3))^2+(y-1)^2=13^2#
Sometimes what is being asked for is the "standard form of the polynomial" and this is somewhat different. The "standard form of the polynomial" is expressed as a sum of terms arranged with decreasing degrees set equal to zero. If this is what your teacher is looking for you will need to expand and rearrange the terms: #color(white)("XXX")x^2+6x+9+y^2-2y+1=169#
#color(white)("XXX")x^2+y^2+6x-2y-159=0#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7