Assertion : The ratio of length of tangent to length of normal is directly proportional…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Assertion : The ratio of length of tangent to length of normal is directly proportional to the ordinate of the point of tangency at the curve y2 = 4ax.
Reason : Length of normal & tangent to a curve
y = f (x) is \[\left|\mathrm{y} \sqrt{1+\mathrm{m}^{2}}\right| \text { and }\left|\frac{\mathrm{y} \sqrt{1+\mathrm{m}^{2}}}{\mathrm{~m}}\right|,\]where \(\mathrm{m}=\frac{\mathrm{dy}}{\mathrm{dx}}\).
Reason : Length of normal & tangent to a curve
y = f (x) is \[\left|\mathrm{y} \sqrt{1+\mathrm{m}^{2}}\right| \text { and }\left|\frac{\mathrm{y} \sqrt{1+\mathrm{m}^{2}}}{\mathrm{~m}}\right|,\]where \(\mathrm{m}=\frac{\mathrm{dy}}{\mathrm{dx}}\).
- If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
- If Assertion is true, Reason is true, Reason is not a correct explanation for Assertion.
- If Assertion is true, Reason is false.
- If Assertion is false, Reason is true.
Answer
(A) If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
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