Chapter 11: Q.85 (page 1102)

In the following exercises, match each graph to one of the following equations:
$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$

Short Answer

Expert verified

The equation of the given graph is $a) x^{2} + y^{2} = 64$

Step by step solution

Step 1. Given Information

Given graph is

Given equations to match are:

$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$

The equation of the given graph among the given equations is to be determined.

Step 2. Equation of the graph

Given graph is a circle.

The standard form of a circle is ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ where $(h, k)$ is the centre and $r$ is the radius of the circle.

Here, from the graph the ends of the diameter of the circle are $(- 8, 0), (8, 0)$ .

So the centre is midpoint of the ends i.e. $(\frac{- 8 + 8}{2}, \frac{0 + 0}{2}) = (0, 0)$

The radius of the circle is half the length of the diameter i.e. $\frac{8 - (- 8)}{2} = \frac{16}{2} = 8$

Plugging the values in the equation of circle:

${(x - h)}^{2} + {(y - k)}^{2} = r^{2} {(x - 0)}^{2} + {(y - 0)}^{2} = 8^{2} x^{2} + y^{2} = 64$

Step 3. Conclusion

The equation of the given graph is $a) x^{2} + y^{2} = 64$

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In the following exercises, match each graph to one of the following equations:
$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equation of the graph

Step 3. Conclusion

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In the following exercises, match each graph to one of the following equations:a)x2+y2=64b)x2+y2=49c)x+52+y+22=4d)x-22+y-32=9e)y=-x2+8x-15f)y=6x2+2x-1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equation of the graph

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Statistics

Applied Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, match each graph to one of the following equations:
$a) x^{2} + y^{2} = 64 b) x^{2} + y^{2} = 49 c) {(x + 5)}^{2} + {(y + 2)}^{2} = 4 d) {(x - 2)}^{2} + {(y - 3)}^{2} = 9 e) y = - x^{2} + 8 x - 15 f) y = 6 x^{2} + 2 x - 1$