Question

Find the equation of the tangents to the circle x^2+y^2=25 which make an angle 60 degree with the positive direction of the y axis

Answer 1

You've found the radius and centre, then let the tangent line be 3x−4y+c=03x−4y+c=0.

The distance of the tangent from the centre is

∣∣∣3(1)−4(2)+c32+42−−−−−−√∣∣∣(c−55)2(c−5)2−152(c−20)(c+10)c=3=32=0=0=20or−10

|3(1)−4(2)+c32+42|=3(c−55)2=32(c−5)2−152=0(c−20)(c+10)=0c=20or−10

The required tangents are:

3x−4y+20=0or3x−4y−10=0

hope this answer helpful u