Photo AI
16 (a) On the grid, draw the graph of $x^2 + y^2 = 12.25$ - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 2
Question 17
16 (a) On the grid, draw the graph of $x^2 + y^2 = 12.25$. (b) Hence find estimates for the solutions of the simultaneous equations $x^2 + y^2 = 12.25$ $2x + y = ... show full transcript
Worked Solution & Example Answer:16 (a) On the grid, draw the graph of $x^2 + y^2 = 12.25$ - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 2
Step 1
Draw the graph of $x^2 + y^2 = 12.25$
Answer
To draw the graph of the equation , we recognize that it represents a circle with a radius of (\sqrt{12.25} = 3.5) centered at the origin (0, 0).
You can plot points at various angles, such as:
- When , (points are (0, 3.5) and (0, -3.5)).
- When , (points are (3.5, 0) and (-3.5, 0)).
- Additionally, points such as (2, 3), (2, -3), (-2, 3), and (-2, -3) can be calculated to provide more accurate plotting points for the circle.
The curve should be smooth and round, showing the complete shape of the circle.
Step 2
Hence find estimates for the solutions of the simultaneous equations
Answer
To estimate the solutions for the simultaneous equations:
- We know from part (a) that the graph of is a circle.
- The second equation, , can be rearranged to find : . This is a straight line.
- To find the points of intersection, we can plot this line on the same graph as the circle.
- The estimates for solutions can be found where the line and the circle intersect each other visually:
- Using the graph, one can estimate the points roughly to be around the coordinates (approximately 1.5, -2) and (-2.5, 6) as potential solutions by observing the intersection of the line with the circle.