IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

SCIENTIST135

Area of triangle formed by the tangent and normal of the circle x²+y²=4 at its point (1, 3^1/2) together with x-axis is ?

raulrag009

Look at the figure.

Eqn of tangent at (1, sqrt{3}

)

x(1)+y(

)=4

intercept at x axis is 4

hypotenuse = 4

By pythogores theorem

16=4+ $x^{2}$ where x is brown line

x=

area =

=

venkat_tatolu

The area of the triangle fromed by the tangent,normal at a point

P(x₁,y₁) on the curve y=f(x) and the line

1) X-axis is y₁²(m²+1)/2m under modulus

2) Y-axis is x₁²(m²+1)/2m under modulus

{where m is dy/dx}