Question

the area of the triangle formed by the positive x axis and the normal and the tangent to the circle x^2+y^2=4 at (1,√3) is​

Answer 1

Step-by-step explanation:

Consider the given equation.

x2+y2=4

We know that the equation of the tangent to the circle x2+y2=Cat point (x1,y1) is is given by

xx1+yy1=C 

So, the equation of the tangent at (1,3) is 

x + 3 y=4        .......... (1)

y=34−3x, it cuts the x axis at (4,0).

Now, equation of normal to the circle is

(y−3) = Slope of normal ×(x−1).

Slope of normal = Slope of tangent−1

So,

Slope of normal = 3

Now, equation of normal is

(y−3)=3 (x−1)

y=3x        .......... (2)

Therefore, in figure 1, the area formed by tangent, normal and x axis will be,

A=∫013