Question

lf the tangent to the curve $f\left(x\right)=x^2$ at any point $(c,f(c\left)\right)$ is parallel to the line joining points $(a,f(a\left)\right)$ and $(b,f(b\left)\right)$ on the curvel then $a,c,b$ are in

• A. AP
• B. GP
• C. HP
• D. AGP

Answer 1

The correct option is A AP

${\partial }^{{}^{\prime }}M=2s$ at $(c,\partial (c\left)\right)=2c$
$\frac{\partial \left(a\right)-\partial \left(L\right)}{a-b}=2c$
$\frac{a^2=b^2}{a-b}=2c$
$a+b=2c$
$\therefore a,c,b$ are in AP