The equation of a curve is $y = x^2$ A is the point where the curve intersects the y-axis - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 3

To determine the center and properties of circle B, we need to find its center after translating circle C. Circle C has the equation:

$x^2 + y^2 = 16$

This indicates a circle with a radius of 4 (since $r^2 = 16 \Rightarrow r = 4$) centered at (0, 0).

Upon translating by the vector (egin{pmatrix} 3 \ 0 \ \ \end{pmatrix}), the center of circle B becomes:

$(0 + 3, 0) = (3, 0)$

The equation of circle B is then:

$(x - 3)^2 + y^2 = 16$

Labeling:

• Center of circle B: (3, 0)
• Points of intersection with the x-axis occur when $y = 0$:

$(x - 3)^2 = 16 \Rightarrow x - 3 = \pm 4$

Thus, $x = 7$ and $x = -1$. The points of intersection are (7, 0) and (-1, 0).

The sketch should include the circle centered at (3, 0) with a radius of 4, clearly labeling the center and points of intersection.