SOLUTION: Show that the line y = 10 − 3x is tangent to the circle x2 + y2 = 10. Find an equation for the line perpendicular to the tangent line at the point of tangency. Show that this lin
Algebra.Com
Question 1157994: Show that the line y = 10 − 3x is tangent to the circle x2 + y2 = 10. Find an equation for the line perpendicular to the tangent line at the point of tangency. Show that this line goes through the center of the circle.
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!
Solve the pair of equations simultaneously. If there is a single solution, then the line and the circle intersect in only one place; that means the line is tangent to the circle.
The system of equations has only one solution: x=3, which makes y=1.
So the point of tangency is (3,1). The slope of the tangent line is -3; the slope of a line perpendicular to it is 1/3. Use the point-slope form of a linear equation.
The y-intercept is 0; that means the line passes through the origin, which is the center of the circle.
RELATED QUESTIONS
Find the equation of the line tangent to the circle x2 + y2 = 25 at point... (answered by Fombitz,htmentor,Boreal,ikleyn,MathTherapy)
Find the equation of the line tangent to a circle x2 + y2 = 13 at... (answered by josgarithmetic)
Find an equation of the line that is tangent to the circle x2 + y2 = 25 at the point... (answered by Alan3354)
The homework question is,Show that the line with equation y=2x-10 is a tangent to the... (answered by scott8148)
Write an equation for the line tangent to the circle x2 + y2 = 17, at the point (4,... (answered by Fombitz)
How do i do question number 77 on 10.3
Write an equation of the line that is tangent to... (answered by jim_thompson5910,Alan3354)
Find the equation of the line tangent to the circle x2 + y2 = 25 at point (-1,5). Use... (answered by josmiceli,solver91311)
Write the equation of the line that is tangent to the circle x2 + y2 = 100 at the point... (answered by josgarithmetic)
Find the equation of the line tangent to the circle x2 + y2 = 36 at point (11,5). Use... (answered by Alan3354)