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Advocard [28]
3 years ago
14

If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?

Mathematics
2 answers:
astraxan [27]3 years ago
5 0

The equation of a circle with center at (a,b) and radius r is: (x-a)^2+(y-b)^2=r^2.

This circle has been translated from (0,0) to (a,b).

 

The equation of the circle in our case can be rewritten as: (x-2)^2+(y-2)^2=2^2

Moving the graph 3 units to the right is: (x-2-3)^2+(y-2)^2=2^2.

Moving the graph 1 unit down is: (x-2-3)^2+(y-2-1)^2=2^2.

This gives the equation: (x-5)^2+(y-3)^2=2^2

<span>So, the center of the circle is: (5,3)</span>

dsp733 years ago
4 0

Answer:  The new co-ordinates of the center are (5, -2).

Step-by-step explanation:  The given equation of a circle is

x^2-4x+y^2+2y=4~~~~~~~~~~~~~~~~~~~~~~~~(i)

We are to find the center of the above circle if the circle (i) is translated 3 units to the right and 1 unit down.

The standard equation of a circle with radius r units and center at (h, k) is given by

(x-h)^2+(y-k)^2=r^2.

From equation (i), we have

x^2-4x+y^2+2y=4\\\\\Rightarrow (x^2-4x+4)+(y^2+2y+1)-4-1=4\\\\\Rightarrow (x-2)^2+(y+1)^2=9\\\\\Rightarrow (x-2)^2+(y+1)^2=3^2.

Comparing the above equation with the standard equation of a circle, we get

center, (h, k) = (2, -1) and radius, r = 3 units.

If the circle is translated 3 units to the right and 1 unit down, then the co-ordinates of the new center will be

(h', k') = (h+3, k-1) = (2+3, -1-1) = (5, -2).

Thus, the new co-ordinates of the center are (5, -2).

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<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

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