Q. 234.0( 4 Votes )

Find the area of

Answer :


As we know that: For a given ellipse we can give the coordinates of a point on the given ellipse by (acos θ, bsin θ)


From figure we can say that length of rectangle = 2a cosθ


Note: In reference to figure - (taking z = θ)


And breadth of inscribed rectangle = 2b sinθ


Let A be the area of rectangle inscribed.


A = 4ab sinθ cos θ = 2ab sin 2θ


We need to maximise the area.




4ab cos 2θ = 0


cos 2θ = 0


θ = π/4


Clearly,


And


θ = π/4 is the point of maxima.


Hence area of the greatest rectangle that can be inscribed in the given ellipse is given by


A = 2ab sin(2×π/4) = 2ab.


OR


Given equation is 3x2 – y2 = 8.


To find the equation of tangent we need to find the slope first and the slope is given by the value of derivative at that point.


As, 3x2 – y2 = 8


Differentiating both sides w.r.t x, we get –






As slope comes to be infinite line is parallel to y – axis


Given that it passes through (4/3,0)


line parallel to y-axis and passing through (4/3,0) is


x = 4/3



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the equationRD Sharma - Volume 1

Find the equationMathematics - Board Papers

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the conditioMathematics - Exemplar