Question

Tangents pa and pb are drawn to the ellipse x^2/16 + y^2/9=1 from the point (0,5). Find the area of triangle pab

Answer 1

Answer:

Given, Equation of the ellipse,

16x2+9y2=1

∴ Chord of contact, 16xx1+9yy1=1⇒16x×0+9y×5=1⇒y=59

Putting y=59 in the above equation of the ellipse,

16x2+9(59)2=1⇒16x2=2516⇒x2=2516×16⇒x=±516

So, A=(516,59),B=(−516,59),P=(0,5)

Since, △PAB is isosceles with base AB

∴Height=(5−59)units=516units

∴ Area of △PAB=21×Base×Height=21×(516+516)×516=25256squareunits.