IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

seraphic

if the common tangent to the parabola y2 = 4ax and the circle x2 + y2 = c2 makes an angle @ with the x-axis then tan²@ = ???

xplain!!

abhishekray07

tan²

=(

c⁴+4a²c²)/2c² - 1/2 ?

seraphic

yeah!

but how?

sunip_the_mini_mastermind

the eqn of tangent to the parabola will be y=mx + a/m.
and eqn of tangent to the circle will be y=mx+c^{[ ]}

(1+m² )
comparing both the eqns we get c²m⁴ +m²c² -a² =0

solving it we get m² =-(c+^{[ ]}

(c⁴ +4a² c² ))/2c²
or tan² @= -(c+^{[ ]}

(c⁴ +4a² c² ))/2c²