Question

the equations of the tangents to the circle x^2+y^2=25 with the slope 2 is

Answer 1

Answer:  2x - y ± 5√5 = 0

Step-by-step explanation is given the enclosed image.

Thanks.

Answer 2

Answer:

Circle equation : $x^2+y^2=25$

To find :

The equations of the tangents with the slope 2

Step-by-step explanation:

let the general equation of a tangent : y = mx + c

where 'm' is the slope and 'c' is y intercept ;

general condition :

=> $c^2 = a^2 (1+m^2)$

for the given circle :

=>  $a^2 = 25$ ;

=> a = 5 ;

given m = 2 ;

=> $c^2 = 25(1 + 2^2) = 25*5 = 125$

=> c = ± 5$\sqrt[]{5}$ ;

Hence, equation of tangents :

y = 2x ± 5√5  

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