Chapter 13: Q. 45 (page 528)

Find the center and the radius of the circle $x^{2} + 4 x + y^{2} - 8 y = 16$ .
(Hint: Express the given equation in the form
${(x - a)}^{2} + {(y - b)}^{2} = r^{2}$ )

Short Answer

Expert verified

The center is (-2, 4) and the radius is 6.

Step by step solution

Step-1 – Given

The given equation is: $x^{2} + 4 x + y^{2} - 8 y = 16$ .

Step-2 – To determine

We have to find the center and radius of the given circle.

Step-3 – Calculation

We first write the equation to the standard form of a circle:

$\begin{array}{l} x^{2} + 4 x + y^{2} - 8 y = 16 \\ x^{2} + 4 x + 4 + y^{2} - 8 y + 16 = 16 + 20 [addbothsides20] \\ [(x^{2}) + 2 (2) (x) + {(2)}^{2}] + [{(y)}^{2} - 2 (4) (y) + {(4)}^{2}] = 36 [perfectsquaretrinomial] \\ {(x + 2)}^{2} + {(y - 4)}^{2} = {(6)}^{2} \end{array}$

The standard form of a circle is: ${(x - a)}^{2} + {(y - b)}^{2} = r^{2}$

Where (a, b) = center and r = radius.

Then we compare the given equation to the standard form of a circle:

$a = - 2, b = 4 and r = 6$ .

So, the center is (-2, 4) and the radius is 6.

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Find the center and the radius of the circle $x^{2} + 4 x + y^{2} - 8 y = 16$ .
(Hint: Express the given equation in the form
${(x - a)}^{2} + {(y - b)}^{2} = r^{2}$ )

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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Find the center and the radius of the circlex2+4x+y2−8y=16.(Hint: Express the given equation in the formx−a2+y−b2=r2)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Find the center and the radius of the circle $x^{2} + 4 x + y^{2} - 8 y = 16$ .
(Hint: Express the given equation in the form
${(x - a)}^{2} + {(y - b)}^{2} = r^{2}$ )