Maths Help GEOMETRY: A circle C is defined by the equation x^2+y^2-8x-4y+10=0

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asred9

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[h=1]Maths Help GEOMETRY: A circle C is defined by the equation x^2+y^2-8x-4y+10=0?[/h]
A circle C is defined by the equation x^2+y^2-8x-4y+10=0
a) Find the coordinates of its center and its radius.
b) Show that the gradient m of the tangents of this circle which pass from the origin obey the equation 10(m^2+1)=(4m-2)^2
c) Hence show that these two tangents are perpendicular.

I found the center which is (4,2) & found also the radius which is 3.16. for part a

Can anyone please help me in b & c. The answers together with how you ended up for that result are highly appreciated.

Thanks
 
asred9 said:
Maths Help GEOMETRY: A circle C is defined by the equation x^2+y^2-8x-4y+10=0?


A circle C is defined by the equation x^2+y^2-8x-4y+10=0
a) Find the coordinates of its center and its radius.
b) Show that the gradient m of the tangents of this circle which pass from the origin obey the equation 10(m^2+1)=(4m-2)^2
c) Hence show that these two tangents are perpendicular.

I found the center which is (4,2) & found also the radius which is 3.16. for part a

Can anyone please help me in b & c. The answers together with how you ended up for that result are highly appreciated.

Thanks
Click to expand...
Part A: complete the square
 
asred9 said:
Hi maybe I wasnt clear but i did part a. I need help in b & c ty
Click to expand...
No, you were clear about having done part a.
part b: What is the form of an equation that crosses the origin? What is the slope of this line. Which of these infinite lines that crosses the origin is tangent to the circle?
 
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