TS EAMCET · Maths · Ellipse
If the line \(2 x-3 y+4=0\) cuts the ellipse \(x=3 \cos \theta\), \(y=5 \sin \theta\) in \(\mathrm{A}\) and \(\mathrm{B}\) and \((\alpha, \beta)\) is the midpoint of \(\overline{\mathrm{AB}}\), then \(3 \beta-2 \alpha=\)
- A –4
- B 4
- C -5
- D 5
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
Given line \(2 x-3 y+4=0\) cuts the ellipse \(x=3 \cos\) \(\theta, y=5 \sin \theta\). Here, \(a=3, b=5\). Required equation of ellipse is \[ \begin{aligned} & \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ & \frac{x^2}{9}+\frac{y^2}{25}=1 . . \end{aligned} \] Satisfy the line…
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