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Q.

Let P be a point in the first quadrant lying on the ellipse 9x2+16y2=144,such that the tangent at P to the ellipse is inclined at an angle 135° to the positive direction of x-axis. Then the coordinates of P are:

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a

1433, 14

b

89, 773

c

42, 32

d

165, 95

answer is D.

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Detailed Solution

Equation of the tangent with slope tan 135° to the ellipse x216+y29=1 is y=−x+16(1)+9⇒x+y=5 which meets the given ellipse at 165,95

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Let P be a point in the first quadrant lying on the ellipse 9x2+16y2=144,such that the tangent at P to the ellipse is inclined at an angle 135° to the positive direction of x-axis. Then the coordinates of P are: