Chapter 11: Q. 177 (page 1135)

In the following exercises, graph each question.
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

Short Answer

Expert verified

Given equation represents a circle with center as $(2, - 5)$ and radius $6$ units.

Step by step solution

Understand the shape of the conic from the given equation.

$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

Since, $x^{2}$ and $y^{2}$ both the terms have the same coefficients, conic will be a circle.

Convert the equation into standard form,

$x^{2} + y^{2} - 4 x + 10 y - 7 = 0 (x^{2} - 4 x + 4) + (y^{2} + 10 y + 25) - 29 - 7 = 0 {(x - 2)}^{2} + {(y + 5)}^{2} - 36 = 0 {(x - 2)}^{2} + {(y + 5)}^{2} = 6^{2}$

Compare this equation with the standard equation of a circle,

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

Where $(h, k)$ is the center of the circle and $r$ is the radius.

Therefore, center of the circle $\to (2, - 5)$

And the radius of the circle = $6$

Graph the equation.

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In the following exercises, graph each question.
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$

Short Answer

Step by step solution

Understand the shape of the conic from the given equation.

Convert the equation into standard form,

Graph the equation.

One App. One Place for Learning.

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In the following exercises, graph each question.x2+y2-4x+10y-7=0

Short Answer

Step by step solution

Understand the shape of the conic from the given equation.

Convert the equation into standard form,

Graph the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Statistics

Mechanics Maths

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each question.
$x^{2} + y^{2} - 4 x + 10 y - 7 = 0$