Shayla Phelps

2023-03-13

How to find the center and radius of the circle given ${x}^{2}+{y}^{2}+8x-6y=0$?

Izabelle Riddle

Beginner2023-03-14Added 3 answers

We need

$(a+b)}^{2}={a}^{2}+2ab+{b}^{2$

$(a-b)}^{2}={a}^{2}-2ab+{b}^{2$

Complete the x and y squares.

${x}^{2}+{y}^{2}+8x-6y=0$

${x}^{2}+8x+{y}^{2}-6y=0$

$x}^{2}+8x+{{\left(\frac{8}{2}\right)}^{2}}+{y}^{2}-6y+{{\left(\frac{6}{2}\right)}^{2}}={{\left(\frac{8}{2}\right)}^{2}}+{{\left(\frac{6}{2}\right)}^{2}$

$x}^{2}+8x+{{\left(4\right)}^{2}}+{y}^{2}-6y+{{\left(3\right)}^{2}}={{\left(4\right)}^{2}}+{{\left(3\right)}^{2}$

$(x+4)}^{2}+{(y-3)}^{2}=25={5}^{2$

This is the equation of a circle, center $(-4,3)$ and radius $=5$

graph{(x^2+y^2+8x-6y)=0 [-15.25, 13.23, -3.42, 10.82]}

$(a+b)}^{2}={a}^{2}+2ab+{b}^{2$

$(a-b)}^{2}={a}^{2}-2ab+{b}^{2$

Complete the x and y squares.

${x}^{2}+{y}^{2}+8x-6y=0$

${x}^{2}+8x+{y}^{2}-6y=0$

$x}^{2}+8x+{{\left(\frac{8}{2}\right)}^{2}}+{y}^{2}-6y+{{\left(\frac{6}{2}\right)}^{2}}={{\left(\frac{8}{2}\right)}^{2}}+{{\left(\frac{6}{2}\right)}^{2}$

$x}^{2}+8x+{{\left(4\right)}^{2}}+{y}^{2}-6y+{{\left(3\right)}^{2}}={{\left(4\right)}^{2}}+{{\left(3\right)}^{2}$

$(x+4)}^{2}+{(y-3)}^{2}=25={5}^{2$

This is the equation of a circle, center $(-4,3)$ and radius $=5$

graph{(x^2+y^2+8x-6y)=0 [-15.25, 13.23, -3.42, 10.82]}

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?

How do I find the y-intercept of a parabola?

What are the vertices of $9{x}^{2}+16{y}^{2}=144$?

How to determine the rate of change of a function?

Why are the tangents for 90 and 270 degrees undefined?

How to find the center and radius of the circle ${x}^{2}+{y}^{2}-6x+8y=0$?

What is multiplicative inverse of a number?

How to find the continuity of a function on a closed interval?

How do I find the tangent line of a function?

How to find vertical asymptotes using limits?

How to find the center and radius of the circle ${x}^{2}-12x+{y}^{2}+4y+15=0$?

Let f be a function so that (below). Which must be true?

I. f is continuous at x=2

II. f is differentiable at x=2

III. The derivative of f is continuous at x=2

(A) I (B) II (C) I and II (D) I and III (E) II and IIIHow to find the center and radius of the circle ${x}^{2}+{y}^{2}+4x-8y+4=0$?

How to identify the center and radius of the circle ${(x+3)}^{2}+{(y-8)}^{2}=16$?

How to evaluate the limit $lim\frac{{e}^{t}}{t}$ as $t\to \infty$?