Question

Assertion(A): If the tangent at any point $P$ on the curve $xy=a^2$ meets the axes at $A$ and $B$ then $AP:PB=1:1$
Reason(R): The tangent at $P(x,y)$ on the curve $X^m.Y^n=a^{m+n}$ meets the axes at $A$ and $B$. Then the ratio of $P$ divides $\overline{AB}$ is $n:m$.

• 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

Answer: (A)

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

$y=\frac{a^2}{x}$
$y^{\prime }=-\frac{a^2}{x^2}$
$y^{\prime }=-\frac{a^2}{t^2}$
$(y-\frac{a^2}{t})=\frac{-a^2}{t^2}(n-t)$
$B=(2+10)$
$A=(0,\frac{2a^2}{t})$
$\frac{AP}{BP}=1$