question_answer

A circle touches the y-axis at the point \[(0,4)\] and passes through the point. Which of the following lines is not a tangent to this circle?                                                    [JEE MAIN Held on 09-01-2020 Morning]

A) \[3x-4y-24=0\]

B) \[4x-3y+17=0\]

C) \[4x+3y-8=0\]

D) \[3x+4y-6=0\]

Correct Answer: C

Solution :

[c] As circle touches the y-axis, let the centre be (r, 4) where r is the radius of the circle \[\because \,\,\,\,\,\,\,\,\,\sqrt{{{\left( r-2 \right)}^{2}}+{{4}^{2}}}={{r}^{2}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,r=5\] Now if a line touches the circle then length of perpendicular from \[(5,4)\] to that line must be equals to 5. Only option is correct