Question

Two common tangent to the circle x²+ y² = 2a² and parabola y² = 8ax are ?

Answer 1

Hi !!! 

Solution :- 

Any tangent to the parabola y² = 8ax is 

y = mx + 2a /m ------(1) 

if ( 1) is a tangent to the circle x² + y² = 2a² 

then , 
= > \sqrt{2a} = + - \frac{2a}{m \sqrt{m ^{2} + 1} }=>2a​=+−mm2+1​2a​ 

=> m² ( 1 + m² ) = 2 

=> ( m² + 2 ) ( m² - 1 ) = 0 

=> m = +- 1 

so from , (1) y = +- ( x + 2a ) 

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Hope it helps !! 

muskraj ❤