Home
Class 12
MATHS
The area of the rectangle formed by the ...

The area of the rectangle formed by the perpendicular from the center of the standard ellipse to the tangent and normal at its point whose eccentric angle is `pi/4`, is

Text Solution

Verified by Experts

The correct Answer is:
`(30)/(13)` sq. units
Equation of tangent at point `P((pi)/(4))` is
`(x)/(3)cos.(pi)/(4)+(y)/(2)sin.(pi)/(4)=1`
or `2x+3y-6sqrt(2)=0`
Equation of normalat P is
`3sqrt(2)x-2sqrt(2)y-5=0`
Distacne of centre from the tangent is `(6sqrt(3))/(sqrt(13))`
Distance of centre from the normal is `(5)/(sqrt(2)sqrt(13))`
`:.` Area of required rectangle `=(6sqrt(2))/(sqrt(13))xx(5)/(sqrt(2)sqrt(13))=(30)/(13)` sq. unit
Promotional Banner

Similar Questions

Explore conceptually related problems

The area of the rectangle formed by the perpendiculars from the centre of the standard ellipse to the tangent and normal at its point whose eccentric angles pi/4 is

The product of the perpendiculars drawn from the two foci of an ellipse to the tangent at any point of the ellipse is

In both an ellipse and hyperbola , prove that the focal distance of any point and the perpendicular from the centre upon the tangent at it meet on a circle whose centre is the focus and whose radius is the semi-transverse axis.

The equation of normal to the ellipse x^(2)+4y^(2)=9 at the point wherr ithe eccentric angle is pi//4 is

Equation of the tangent to the hyperbola 4x^(2)-9y^(2)=1 with eccentric angle pi//6 is

Area of the triangle formed by the tangents at the point on the ellipse x^2/a^2+y^2/b^2=1 whose eccentric angles are alpha,beta,gamma is

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , is

The locus of the point of intersection of tangents to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 at the points whose eccentric angles differ by pi//2 , is

The locus of the point of intersection of tangents to the circle x=a cos theta, y=a sin theta at points whose parametric angles differ by pi//4 is

Let x + 6y = 8 is tangent to standard ellipse where minor axis is 4/sqrt3 , then eccentricity of ellipse is