Question

Write an equation for the translation of x^2+y^2=49 by 3 units left and 4 units up

Answer 1

(x+3)^2+(y-4)^2=49
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Answer 2

Answer:

  $(x+3)^2+(y-4)^2=49$

Step-by-step explanation:

Given : $x^2+y^2=49$

To Find: Write an equation for the translation of $x^2+y^2=49$   by 3 units left and 4 units up.

Solution:

$x^2+y^2=49$

$y^2=49-x^2$

$y=\sqrt{49-x^2}$

So, $f(x)=y=\sqrt{49-x^2}$

We are given that first is shifted towards 3 units left.

If the given function f(x) translated by b units left then

f(x)→f(x+b)

So, $f(x)=\sqrt{49-x^2}$ translated by 3 units left

So, $f(x)=\sqrt{49-x^2}$ → $f(x+3)=\sqrt{49-(x+3)^2}$

Now it is again translated by 4 units up.

If the given function f(x) translated by b units up then

f(x)→f(x)+b

$f(x+3)=\sqrt{49-(x+3)^2}$→ $f(x+3) +4 =\sqrt{49-(x+3)^2 }+4$

So, the function becomes : $f(x)=y=\sqrt{49-(x+3)^2 }+4$

                                              $y-4=\sqrt{49-(x+3)^2 }$  

                                              $(y-4)^2=49-(x+3)^2$  

                                              $(x+3)^2+(y-4)^2=49$

Hence an equation for the translation of $x^2+y^2=49$   by 3 units left and 4 units up is     $(x+3)^2+(y-4)^2=49$