WBJEE · Maths · Differentiation
The points of the ellipse \(16 x^{2}+9 y^{2}=400\) at which the ordinate decreases at the same rate at which the abscissa increases is/are given by
- A \(\left(3, \frac{16}{3}\right)\) and \(\left(-3,-\frac{16}{3}\right)\)
- B \(\left(3,-\frac{16}{3}\right)\) and \(\left(-3, \frac{16}{3}\right)\)
- C \(\left(\frac{1}{16}, \frac{1}{9}\right)\) and \(\left(-\frac{1}{16},-\frac{1}{9}\right)\)
- D \(\left(\frac{1}{16},-\frac{1}{9}\right)\) and \(\left(-\frac{1}{16}, \frac{1}{9}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(3, \frac{16}{3}\right)\) and \(\left(-3,-\frac{16}{3}\right)\)
Step-by-step Solution
Detailed explanation
Given that, the ordinate decreases at the same rate at which the abscissa increases, therefore \[ \frac{d y}{d t}=-\frac{d x}{d t} \] Also, equation of ellipse \[ 16 x^{2}+9 y^{2}=400 \] On differentiating wrt. \(t\), we get…
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