Conic Sections Question 133
Question: The equation of common tangents to the parabola $ y^{2}=8x $ and hyperbola $ 3x^{2}-y^{2}=3 $ , is
Options:
A) $ 2x\pm y+1=0 $
B) $ 2x\pm y-1=0 $
C) $ x\pm 2y+1=0 $
D) $ x\pm 2y-1=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Tangent to $ y^{2}=8x $
therefore $ y=mx+\frac{2}{m} $
Tangent to $ \frac{x^{2}}{1}-\frac{y^{2}}{3}=1 $
therefore $ y=mx\pm \sqrt{r^{2}-m^{2}} $
On comparing, we get m = ±2 or tangent line as
BETA
