Photo AI

A circle C has centre ($-1, 7$) and passes through the point $(0, 0)$ - Edexcel - A-Level Maths Pure - Question 3 - 2012 - Paper 4

Question icon

Question 3

A-circle-C-has-centre-($-1,-7$)-and-passes-through-the-point-$(0,-0)$-Edexcel-A-Level Maths Pure-Question 3-2012-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 3 - 2012 - Paper 4

Step 1

Find the Radius of the Circle

96%

114 rated

Answer

The radius can be calculated by using the distance formula between the center of the circle and the given point. The distance formula is given as:

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

Here, the center is (−1,7)(-1, 7) and the point is (0,0)(0, 0). Therefore, substituting into the formula gives:

r=sqrt(0−(−1))2+(0−7)2=sqrt(1)2+(−7)2=sqrt1+49=sqrt50r = \\sqrt{(0 - (-1))^2 + (0 - 7)^2} = \\sqrt{(1)^2 + (-7)^2} = \\sqrt{1 + 49} = \\sqrt{50}

Step 2

Write the Equation of the Circle

99%

104 rated

Answer

The standard form of the equation of a circle is:

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

Where (h,k)(h, k) is the center of the circle and rr is the radius. Here, the center is (−1,7)(-1, 7) and the radius found is sqrt50\\sqrt{50}. Thus, substituting these values in we get:

(x−(−1))2+(y−7)2=( sqrt50)2(x - (-1))^2 + (y - 7)^2 = (\,\\sqrt{50})^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

;