KCET · Maths · Application of Derivatives
The length of the subtangent, ordinate and the subnormal are in
- A \(\mathrm{AP}\)
- B HP
- C GP
- D Arithmetico-geometric progression
Answer & Solution
Correct Answer
(C) GP
Step-by-step Solution
Detailed explanation
\(\because \quad\) Subtangent \(=\mathrm{y} \times \frac{\mathrm{dx}}{\mathrm{dy}}\)
and subnormal \(=\mathrm{y} \times \frac{\mathrm{dy}}{\mathrm{dx}}\)
\(\therefore\) Subtangent \(\times\) subnormal \(=y^{2}=(\text { ordinate })^{2}\)
Hence, length of the subtangent, ordinate and the subnormal are in GP.
and subnormal \(=\mathrm{y} \times \frac{\mathrm{dy}}{\mathrm{dx}}\)
\(\therefore\) Subtangent \(\times\) subnormal \(=y^{2}=(\text { ordinate })^{2}\)
Hence, length of the subtangent, ordinate and the subnormal are in GP.
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