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If the normal at any point P of the ellipse (x^(2))/(16)+(y^(2))/(9) =1 meets the coordinate axes at M and N respectively, then |PM|: |PN| equals |
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Answer» `4:3` `4x sec theta - 3y cosec theta =7` This meets the coordinate axes at `M ((7)/(4) cos theta, 0), N (0,-(7)/(3) SIN theta)` `:. PM^(2) = (4-(7)/(4))^(2) cos^(2) theta + 9 sin^(2) theta` `= (9)/(16) (9 cos^(2) theta + 16sin^(2) theta)` `PN^(2) = 16 cos^(2) theta + (3+(7)/(3))^(2) sin theta` `= (16)/(9) (9 cos^(2) theta + 16 sin^(2) theta)` `:. PM^(2): PN^(2) = 9^(2): 16^(2)` `rArr |PM| : |PN| = 9: 16` |
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