Applications-Of-Derivatives Question 460
Question: An equation of the tangent to the curve $ y=x^{4} $ from the point (2, 0) not on the curve is
[RPET 2000]
Options:
A) $ y=0 $
B) $ x=0 $
C) $ x+y=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let the point of contact be $ (h,k) $ , where $ k=h^{4} $ . Tangent is $ y-k=4h^{3}(x-h) $ , $ [ \because ,\frac{dy}{dx}=4x^{3} ] $ It passes through (2, 0), \ $ -k=4h^{3}(2-h) $ $ $
Þ $ h=0 $ or 8/3 , \ $ k=0 $ or (8/3)4 \ Points of contact are (0, 0) and $ ( \frac{8}{3},,{{( \frac{8}{3} )}^{4}} ) $ \ Equation of tangents are $ y=0 $ and $ y-{{( \frac{8}{3} )}^{4}}=4{{( \frac{8}{3} )}^{3}}( x-\frac{8}{3} ) $ .
BETA
