Circle And System Of Circles Question 67
Question: Consider the following statements : Assertion : The circle $ x^{2}+y^{2}=1 $ has exactly two tangents parallel to the x-axis Reason (R) : $ \frac{dy}{dx}=0 $ on the circle exactly at the point $ (0,\pm 1) $ . Of these statements
[SCRA 1996]
Options:
A) $ 3x+4y=\pm 2\sqrt{5} $
B) $ 6x+8y=\pm \sqrt{5} $
C) $ 3x+4y=\pm \sqrt{5} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Equation of tangent $ y=\frac{-3}{4}x\pm \frac{1}{\sqrt{5}}\sqrt{1+{{( \frac{-3}{4} )}^{2}}} $
therefore $ y=\frac{-3}{4}x\pm \frac{1}{\sqrt{5}}\sqrt{\frac{16+9}{16}} $
therefore $ 4y=-3x\pm \sqrt{5}\Rightarrow 3x+4y=\pm \sqrt{5} $
BETA
