I don't know how to do
in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

The red circle is the one given. 

The equation of the circle can be rewritten by completing the squares.

(x-1)²=x²-2x+1 so x²-2x=(x-1)²-1 and (y-3)²=y²-6y+9, so y²-6y=(y-3)²-9.

Therefore: (x-1)²-1+(y-3)²-9+5=0, (x-1)²+(y-3)²=5, which is a circle radius √5, centre O(1,3) (see picture). The origin is C(0,0)

OC=√(1+9)=√10. OB=OA=√5 (radius). Tangent AC is perpendicular to OA, and tangent BC is perpendicular to OB.

The line L touches the circle at two points A and B. To find them we need to draw another circle (blue). The radius is AC, AC²=OC²-OA²=10-5=5, so the equation of the blue circle is x²+y²=5. This circle intersects the other ((x-1)²+(y-3)²=5) at A and B. 

So x²+y²=(x-1)²+(y-3)²=5, x²-(x-1)²+y²-(y-3)²=0, 2x-1+6y-9=0, 2x+6y=10, x+3y=5. Therefore x=5-3y, and we can substitute in x²+y²=5, (5-3y)²+y²=5, 25-30y+10y²=5, 10y²-30y+20=0, y²-3y+2=0=(y-1)(y-2), so the y coords of the points are 1 and 2. So corresponding x values are 5-3=2 and 5-6=-1. The points are A(2,1) and B(-1,2) (see picture). The equation of L are of the form y=mx, so plug in each point to find m: 1=2m, m=½ and 2=-m, m=-2, so L is y=x/2 or y=-2x.

by Top Rated User (737k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
84,769 questions
89,821 answers
29,938 users