Question

The subtangent, ordinate and subnormal to the parabola $y^2=4ax$ at a point (different from origin) are in

• A. AP
• B. HP
• C. GP
• D. AGP

Answer 1

Answer: (C)

GP

Let $S_t,S_n$ represents length of tangent and sub-normal to the

parabola $y^2=4ax$

Let $(x_1,y_1)$ be any point different from origin

Length of sub-tangent $=\frac{y}{y_1}=S_t$

Length of sub-normal $=y{y}_1=S_n$

Ordinate $=y$

Now, $S_t\times S_n=y^2$

If we take, three of them in order i.e. $\frac{y}{y_1},y,y{y}_1$ obtained by multiplying $y_1$ to the previous term. So, they are in series with a common ratio of $y_1$

Hence, subtangent, ordinate, subnormal are in $G.P$