Let C1 be the circle centre P=(−1,1) with radius 17 17 and C2 be the circle centre Q=(1,−1) with radius 13. (a) Determine an equation for each of C1 and C2 in the form x 2+Ax+y 2+By+C=0. (b) Determine the two points of intersection R, S of the circles C1 and C2.

Question

Let C1 be the circle centre P=(−1,1) with radius 17   17 and C2 be the circle centre   Q=(1,−1) with radius 13.   (a) Determine an equation for each of C1 and C2 in the form x   2+Ax+y   2+By+C=0.   (b) Determine the two points of intersection R, S of the circles C1 and C2.

averes8 · Accepted Answer

Step 1 C1 be the circle center P=(−1,1) with radius 17 C2 be the circle center Q=(1,−1) with radius 13 a) To determine the equation of each circle. b) To find the points of intersection of C1 and C2. Step 2 a) C1:(x+1)2+(y−1)2=(17)2 ⇒x2+2x+1+y2−2y+1=17 ∴x2+y2+2x−2y−15=0 C2:(x−1)2+(y+1)2=(13)2 ⇒x2−2x+1+y2+2y+1=13 ∴x2+y2−2x+2y−11=0 Step 3 b) For the points of intersection, we equate the equations of C1 and C2. ⇒x2+y2+2x−2y−15=x2+y2−2x+2y−11 ⇒4x−4y=15−11 ⇒4x−4y=4 ⇒x−y=1 ∴x=y+1 Step 4 Put this value in the equation of C1, ⇒(y+1)2+y2+2(y+1)−2y−15=0 ⇒y2+2y+1+y2+2y+2−2y−15=0 ⇒2y2+2y−12=0 ⇒y2+y−6=0 ⇒y2+3y−2y−6=0 ⇒y(y+3)−2(y+3)=0 ⇒(y+3)(y−2)=0 ∴y=−3,y=2 y=−3⇒x=−3+1=−2 y=2⇒x=2+1=3 Therefore points of intersection: R=(−2,−3) S=(3,2)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Let C1 be the circle centre P = (−1, 1) with radius \sqrt{17}

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