M(-3; 4) is the centre of the large circle and a point on the small circle having centre 0(0,0). From N(-11;p), a tangent is drawn to touch the large circle at T with NT is parallel to the
J-axis. NM is a tangent to the smaller circle at M with MOS a diameter,
у
T T
M(-3; 4)
N(-11; p)
S
Determine the equation of the small circle.​

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: