SOLUTION: Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. 𝑥2+𝑦2−8𝑥+14𝑦+65=36

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. 𝑥2+𝑦2−8𝑥+14𝑦+65=36      Log On


   

Question 744884: Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle.
𝑥2+𝑦2−8𝑥+14𝑦+65=36
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2-8x%2B14y%2B65=36.......write 65 as 16%2B49
x%5E2%2By%5E2-8x%2B14y%2B16%2B49=36.....group
%28x%5E2-8x%2B16%29%2B%28y%5E2%2B14y%2B49%29=36
%28x-4%29%5E2%2B%28y%2B7%29%5E2=36
so, h=4, k=-7, r=6
the center is at: (4,-7)
radius: r=6
x-intercepts occur when y+=+0
%28x-4%29%5E2%2B%280%2B7%29%5E2=36
x%5E2-8x%2B16%2B49=36
x%5E2-8x%2B65-36=0
x%5E2-8x%2B29=0..use quadratic formula
x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A1%2A29+%29%29%2F%282%2A1%29+
x+=+%288+%2B-+sqrt%2864-116+%29%29%2F2+
x+=+%288+%2B-+sqrt%28-52+%29%29%2F2+
solutions: imaginary, no x-intercepts


y-intercepts occur when x+=+0
%280-4%29%5E2%2B%28y%2B7%29%5E2=36
16%2B%28y%2B7%29%5E2=36
16%2By%5E2%2B14y%2B49=36
y%5E2%2B14y%2B65-36=0
y%5E2%2B14y%2B29=0

y+=+%28-14+%2B-+sqrt%28+14%5E2-4%2A1%2A29+%29%29%2F%282%2A1%29+
y+=+%28-14+%2B-+sqrt%28196-116+%29%29%2F2+
y+=+%28-14+%2B-+sqrt%2880+%29%29%2F2+
y+=+%28-14+%2B-+8.94%29%2F2+
solutions:
y+=+%28-14+%2B+8.94%29%2F2+
y+=+-5.06%2F2+
y+=+-2.53+
and
y+=+%28-14-8.94%29%2F2+
y+=+-22.94%2F2+
y+=+-11.47