Question

The equation of a circle is x^2 + y^2 =16 if the circle is translated 2 units up, what is the equation of the new circle?

Answer 1

The equation of the circle with the new point will be x² + ( y - 2 )² = 16.

What is a circle?

The circle is defined as the locus of the point traces around a fixed point called the centre and is equidistant from the outer trace.

Given that:-

• The circle is translated as 2 units up.

The equation of the circle will be formed as:-

We know that the general form of the circle is given as

( x - h )² + ( y - k )² = r²,

where ( h, k ) is the centre and r is the radius. When the circle is shifted 2 units up it means that now its centre will be ( 0, 2). So the equation will be:-

x² + ( y - 2 )² = 16

Therefore the equation of the circle with the new point will be x² + ( y - 2 )² = 16.

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