Question

Write an equation in standard form for the circle. ( x - 3) 2 + ( y + 5) 2 = 64

Answer 1

The standard form:
$(x-3)^2+(y+5)^2=64$.
Use:  $(a\pm b)^2=a^2\pm2ab+b^2$.
$x^2-2\cdot x\cdot3+3^2+y^2+2\cdot y\cdot5+5^2=64\\\\x^2-6x+9+y^2+10y+25=64\ \ \ |-64\\\\x^2+y^2-6x+10y-39=0$
.
The general form.

Answer 2

Answer:

The equation $(x-3)^2+(y+5)^2=64$   in standard form for the circle is $(x-3)^2+(y-(-5))^2=8^2$

Step-by-step explanation:

Given : Equation of circle as  $(x-3)^2+(y+5)^2=64$

We have to write the equation in standard form for the circle.

 

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

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

Consider the given equation  $(x-3)^2+(y+5)^2=64$

64 can be written as 8²

Rewrite it in standard form as ,

$(x-3)^2+(y-(-5))^2=8^2$

where center is (3, - 5) and radius = 8

Thus, The equation $(x-3)^2+(y+5)^2=64$   in standard form for the circle is $(x-3)^2+(y-(-5))^2=8^2$