1. Tardigrade
  2. Question
  3. Mathematics
  4. Statement-I: Tangent drawn at a point P((4 √5/3), 2) on the ellipse 9 x2+16 y2=144 intersects a straight line x =(16/√7) at M, then PM subtends a right angle at (-√7, 0) Because Statement-II: The portion of the tangent to an ellipse between the point of contact and the directrix subtends a right angle at the corresponding focus.

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Q. Statement-I : Tangent drawn at a point $P\left(\frac{4 \sqrt{5}}{3}, 2\right)$ on the ellipse $9 x^2+16 y^2=144$ intersects a straight line $x =\frac{16}{\sqrt{7}}$ at $M$, then $PM$ subtends a right angle at $(-\sqrt{7}, 0)$ Because
Statement-II : The portion of the tangent to an ellipse between the point of contact and the directrix subtends a right angle at the corresponding focus.

Conic Sections

Solution:

Correct answer is (d) Statement-I is false, Statement-II is true.