Answer:
In the point (-4,3) tangent is : y=4/3x+25/3 i.e, y=1.33x+8.33
In the point (-4,-3) tangent is: y=-4/3x-25/3 i.e, y=-1.33x-8.33
Step-by-step explanation:
The center of the circle is in (0,0), because x^2+y^2=(x-0)^2+(y-0)^2=25. And the radius is 5, because 5^2=25.
We have first center: (x1,y1)=(0,0)
The point of the tangent is in x=-4, so x^2+y^2=25 is 16+y^2=25,i.e y=3 and y=-3. Like you can see we have 2 tangents to the circle when x=-4. the point (-4,3) and (-4,-3).
We will do for the first point:
The point of tangent is (x2,y2)=(-4,3)
The gradient of the radius
mr=(y2-y1)/(x2-x1)=(3-0)/(-4-0)=-3/4
The gradient of the tangent mt is:
mr*mt=-1 (they are ortogon)
mt=-1/mr=-1/(-3/4)=4/3
the equation of the line trought one point is:
y-y2=k(x-x2), where k is mt,i.e. k=4/3
y-3=4/3(x-(-4))
y=4/3x+16/3+3
y=4/3x+25/3
y=1.33x+8.33
Now for the 2nd point (-4,-3),
mr=-3/-4=3/4
mt=-4/3
y+3=-4/3(x-(-4))
y=-4/3x-16/3-3
y=-4/3x-25/3
y=-1.33x-8.33
