Question

find the ratio in which the line joining the points (6,12) and (4,9) is divided by the curve x^2+y^2=4​

Answer 1

Step-by-step explanation:

The equation of the line

slope  m  =3/2

Equation be y= (3÷2)x + c

Substituting the points (4,9) in the above equation we get

 9 = 6 + c

c=3

Equation of the line y = (3÷2)x + 3

Substituting the value of y in the equation of the curve we get

(3x÷2+3)² +x²= 4

9x²÷4 + 9 +9x=4

9x²÷4 + 9x+5=0

x=  (-9 + √81-45) ÷ (9÷2)

  = -9+6÷4.5

= -2÷3  or  -10÷3

As the value of x is known, we can substitue this value of x in the equation of curve and find the value of y, as  both the coordinates of the points are known, we can calculate the ration in which the curve divides the two lines.