Photo AI

A circle C has centre (–1, 7) and passes through the point (0, 0) - Edexcel - A-Level Maths Pure - Question 4 - 2012 - Paper 4

Question icon

Question 4

A-circle-C-has-centre-(–1,-7)-and-passes-through-the-point-(0,-0)-Edexcel-A-Level Maths Pure-Question 4-2012-Paper 4.png

A circle C has centre (–1, 7) and passes through the point (0, 0). Find an equation for C.

Worked Solution & Example Answer:A circle C has centre (–1, 7) and passes through the point (0, 0) - Edexcel - A-Level Maths Pure - Question 4 - 2012 - Paper 4

Step 1

Find the Radius of the Circle

96%

114 rated

Answer

To find the radius of the circle, we can use the distance formula between the center of the circle, (-1, 7), and the point it passes through, (0, 0). The formula is given by:

r=extdistance=sqrt(x2−x1)2+(y2−y1)2r = ext{distance} = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Substituting the points: r=sqrt(0−(−1))2+(0−7)2=sqrt(1)2+(−7)2=sqrt1+49=sqrt50=5sqrt2r = \\sqrt{(0 - (-1))^2 + (0 - 7)^2} = \\sqrt{(1)^2 + (-7)^2} = \\sqrt{1 + 49} = \\sqrt{50} = 5\\sqrt{2}

Step 2

Write the Equation of the Circle

99%

104 rated

Answer

The standard equation of a circle with center (h, k) and radius r is:

(x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2

Substituting h = -1, k = 7, and r = 5\sqrt{2}$:

(x+1)2+(y−7)2=(5sqrt2)2(x + 1)^2 + (y - 7)^2 = (5\\sqrt{2})^2

This simplifies to:

(x+1)2+(y−7)2=50(x + 1)^2 + (y - 7)^2 = 50

Join the A-Level students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;