Question

Assertion A: The curves $x^2=y,x^2=-y$ touch each other at (0, 0).
Reason R: The slopes of the tangents at (0, 0) for both the curves are equal.

• A. Both A and R are true R is the correct explanation of A
• B. Both A and R are true but R is not correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is A Both A and R are true R is the correct explanation of A

$y^{\prime }=2x$
$y^{\prime }{|}_{x=0}=0=m_1$
$y^{\prime }=-2x$
$y^{\prime }{|}_{x=0}=0=m_2$
$m_1=m_2$
$\therefore$ both the curve touches each other