Photo AI

Find the exact coordinates of the two intersections of the line $y = 2x$ and the circle $x^2 + y^2 = 30$. - OCR - GCSE Maths - Question 17 - 2018 - Paper 6

Question icon

Question 17

Find-the-exact-coordinates-of-the-two-intersections-of-the-line-$y-=-2x$-and-the-circle-$x^2-+-y^2-=-30$.-OCR-GCSE Maths-Question 17-2018-Paper 6.png

Find the exact coordinates of the two intersections of the line $y = 2x$ and the circle $x^2 + y^2 = 30$.

Worked Solution & Example Answer:Find the exact coordinates of the two intersections of the line $y = 2x$ and the circle $x^2 + y^2 = 30$. - OCR - GCSE Maths - Question 17 - 2018 - Paper 6

Step 1

Substitute the line equation into the circle equation

96%

114 rated

Answer

To find the points of intersection, substitute y=2xy = 2x into the circle's equation:

x2+(2x)2=30x^2 + (2x)^2 = 30

This simplifies to:

x2+4x2=30x^2 + 4x^2 = 30

or

5x2=305x^2 = 30

Step 2

Solve for x

99%

104 rated

Answer

Now solve for xx:

x2=6x^2 = 6

Taking the square root gives us two possible values:

x = rac{ ext{sqrt}(6)}{1} ext{ and } x = - rac{ ext{sqrt}(6)}{1}

Step 3

Find corresponding y coordinates

96%

101 rated

Answer

Next, substitute these xx values back into the line equation to find the corresponding yy values:

For x=extsqrt(6)x = ext{sqrt}(6): y=2(extsqrt(6))=2extsqrt(6)y = 2( ext{sqrt}(6)) = 2 ext{sqrt}(6)

For x=−extsqrt(6)x = - ext{sqrt}(6): y=2(−extsqrt(6))=−2extsqrt(6)y = 2(- ext{sqrt}(6)) = -2 ext{sqrt}(6)

Step 4

Provide the final coordinate answers

98%

120 rated

Answer

Thus, the exact coordinates of the two intersections are:

(extsqrt(6),2extsqrt(6))extand(−extsqrt(6),−2extsqrt(6))( ext{sqrt}(6), 2 ext{sqrt}(6)) ext{ and } (- ext{sqrt}(6), -2 ext{sqrt}(6))

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;